Mathematical Physics, Analysis and Geometry最新文献

{"title":"Baker–Akhiezer Specialisation of Joint Eigenfunctions for Hyperbolic Relativistic Calogero–Moser Hamiltonians","authors":"Martin Hallnäs","doi":"10.1007/s11040-026-09548-0","DOIUrl":"10.1007/s11040-026-09548-0","url":null,"abstract":"<div><p>In earlier joint work with Ruijsenaars, we constructed and studied symmetric joint eigenfunctions <span>(J_N)</span> for quantum Hamiltonians of the hyperbolic relativistic <i>N</i>-particle Calogero–Moser system. For generic coupling values, they are non-elementary functions that in the <span>(N=2)</span> case essentially amount to a ‘relativistic’ generalisation of the conical function specialisation of the Gauss hypergeometric function <span>({}_2F_1)</span>. In this paper, we consider a discrete set of coupling values for which the solution to the joint eigenvalue problem is known to be given by functions <span>(psi _N)</span> of Baker–Akhiezer type, which are elementary, but highly nontrivial, functions. Specifically, we show that <span>(J_N)</span> essentially amounts to the antisymmetrisation of <span>(psi _N)</span> and, as a byproduct, we obtain a recursive construction of <span>(psi _N)</span> in terms of an iterated residue formula.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"29 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-026-09548-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147362874","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Parabolic Gap Theorems for the Yang-Mills Energy","authors":"Anuk Dayaprema,&nbsp;Alex Waldron","doi":"10.1007/s11040-026-09549-z","DOIUrl":"10.1007/s11040-026-09549-z","url":null,"abstract":"<div><p>We prove parabolic versions of several known gap theorems in classical Yang-Mills theory. On an <span>({text {SU} }(r))</span>-bundle of charge <span>(kappa )</span> over the 4-sphere, we show that the space of all connections with Yang-Mills energy less than <span>(4 pi ^2 left( |kappa | + 2 right) )</span> deformation-retracts under Yang-Mills flow onto the space of instantons, allowing us to simplify the proof of Taubes’s path-connectedness theorem. On a compact quaternion-Kähler manifold with positive scalar curvature, we prove that the space of pseudo-holomorphic connections whose <span>(mathfrak {s}mathfrak {p}(1))</span> curvature component has small Morrey norm deformation-retracts under Yang-Mills flow onto the space of instantons. On a nontrivial bundle over a compact manifold of general dimension, we prove that the infimum of the scale-invariant Morrey norm of curvature is positive.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"29 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-026-09549-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147335770","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quasi-Invariant States for Actions of Semidirect Product Groups","authors":"Ali Jabbari","doi":"10.1007/s11040-026-09553-3","DOIUrl":"10.1007/s11040-026-09553-3","url":null,"abstract":"<div><p>We extend the theory of quasi-invariant states for compact group actions on <span>(C^{*})</span>-algebras to the setting of semidirect product groups. Given a compact semidirect product <span>(K=Grtimes _{phi }H)</span>, where <span>(phi )</span> is a continuous homomorphism from <i>H</i> into <span>(operatorname {Aut}(G))</span>, we characterize actions of <i>K</i> on <span>(C^{*})</span>-algebras in terms of compatible actions of the component groups <i>G</i> and <i>H</i>. We establish the fundamental properties of <i>K</i>-quasi-invariant states, including cocycle identities, lifting to von Neumann algebras, averaging properties, and prove the main result that under appropriate modular commutation conditions, the GNS representation of a quasi-invariant state is unitarily equivalent to that of its averaged state. This generalizes the framework established by Griseta [3] for single compact groups.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"29 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147342555","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Some Results on Calibrated Submanifolds in Euclidean Space of Cohomogeneity One and Two","authors":"Faisal Romshoo","doi":"10.1007/s11040-026-09552-4","DOIUrl":"10.1007/s11040-026-09552-4","url":null,"abstract":"<div><p>We construct calibrated submanifolds in Euclidean space invariant under the action of a Lie group <i>G</i>. We first demonstrate the method used in this paper by reproducing the results about special Lagrangians in Harvey-Lawson (Harvey, R. and Blaine Lawson, H.: Acta Math. <b>148</b>, 47–157 1982). We then show explicitly that an associative submanifold in <span>(mathbb {R}^7)</span> invariant under the action of a maximal torus <span>(mathbb {T}^2 subset textrm{G}_2)</span> has to be a special Lagrangian submanifold in <span>(mathbb {C}^3)</span>. Similarly, we also show that a Cayley submanifold in <span>(mathbb {R}^8)</span> invariant under the action of a maximal torus <span>(mathbb {T}^3 subset text {Spin}(7))</span> has to be a special Lagrangian submanifold in <span>(mathbb {C}^4)</span>. We construct coassociative submanifolds in <span>(mathbb {R}^7)</span> invariant under the action of <span>(textrm{Sp}(1)subset mathbb {H})</span> with a more general ansatz than the one in (Harvey, R. and Blaine Lawson, H.: Acta Math. <b>148</b>, 47–157 1982) but we recover exactly the <span>(textrm{Sp}(1))</span>-invariant coassociatives in (Harvey, R. and Blaine Lawson, H.: Acta Math. <b>148</b>, 47–157 1982), giving us a rigidity result. Finally, we construct cohomogeneity two examples of coassociative submanifolds in <span>(mathbb {R}^7)</span> which are invariant under the action of a maximal torus <span>(mathbb {T}^2 subset textrm{G}_2)</span>.\u0000</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"29 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147341622","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Initial Value Space of the Four Dimensional Painlevé System with ((A_5+A_1)^{(1)}) Symmetry","authors":"Kazuya Matsugashita,&nbsp;Takao Suzuki","doi":"10.1007/s11040-026-09551-5","DOIUrl":"10.1007/s11040-026-09551-5","url":null,"abstract":"<div><p>The initial value spaces of the Painlevé equations are proposed by Okamoto. They are symplectic manifolds in which the Painlevé equations are described as polynomial Hamiltonian systems on all coordinates. In this article, we construct an initial value space of the four dimensional Painlevé system with affine Weyl group symmetry of type <span>((A_5+A_1)^{(1)})</span>.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"29 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-026-09551-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147341148","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Heat Kernel on Warped Products","authors":"Ivan G. Avramidi","doi":"10.1007/s11040-026-09550-6","DOIUrl":"10.1007/s11040-026-09550-6","url":null,"abstract":"<div><p>We study the spectral properties of the scalar Laplacian on a <i>n</i>-dimensional warped product manifold <span>(M=Sigma times _f N)</span> with a <span>((n-1))</span>-dimensional compact manifold <i>N</i> without boundary, a one dimensional manifold <span>(Sigma )</span> without boundary and a warping function <span>(fin C^infty (Sigma ))</span>. We consider two cases: <span>(Sigma =S^1)</span> when the manifold <i>M</i> is compact, and <span>(Sigma =mathbb {R})</span> when the manifold <i>M</i> is non-compact. In the latter case we assume that the warping function <i>f</i> is such that the manifold <i>M</i> has two cusps with a finite volume. In particular, we study the case of the warping function <span>(f(y)=[cosh (y/b)]^{-2nu /(n-1)})</span> in detail, where <span>(yin mathbb {R})</span> and <i>b</i> and <span>(nu )</span> are some positive parameters. We study the properties of the spectrum of the Laplacian in detail and show that it has both the discrete and the continuous spectrum. We compute the resolvent, the eigenvalues, the scattering matrix, the heat kernel and the regularized heat trace. We compute the asymptotics of the regularized heat trace of the Laplacian on the warped manifold <i>M</i> and show that some of its coefficients are global in nature expressed in terms of the zeta function on the manifold <i>N</i>.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"29 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-026-09550-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147339392","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Integrable Deformations of Cluster Maps of Type (D_{2N})","authors":"Wookyung Kim","doi":"10.1007/s11040-026-09545-3","DOIUrl":"10.1007/s11040-026-09545-3","url":null,"abstract":"<div><p>In this paper, we extend one of the main results from our joint work [12] with Hone and Mase, in which we studied a deformed type <span>(D_{4})</span> map, to the general case of type <span>(D_{2N})</span> for <span>(Nge 3)</span>. This can be achieved through a “local expansion\" operation, introduced in our joint work [7] with Grabowski and Hone. This operation involves inserting a specific subquiver into the quiver arising from the Laurentification of the deformed type <span>(D_{4})</span> map. This insertion yields a new quiver, obtained through the Laurentification of the deformed type <span>(D_{6})</span> map and thus enables systematic generalization to higher ranks <span>(D_{2N})</span>. We also study the degree growth of the deformed type <span>(D_{2N})</span> map via the tropical method and conjecture that, for each <i>N</i>, the deformed map is integrable, as indicated by the algebraic entropy test, a criterion for detecting integrability in discrete dynamical systems.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"29 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-026-09545-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147337271","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Almost Ricci Solitons Structures on Riemannian Submanifolds of the Euclidean Space","authors":"Hana Al-Sodais,&nbsp;Nasser Bin Turki,&nbsp;Sharief Deshmukh","doi":"10.1007/s11040-026-09546-2","DOIUrl":"10.1007/s11040-026-09546-2","url":null,"abstract":"<div><p>In this article, we explore the possibility of inheriting an almost Ricci soliton structure on a compact Riemannian manifold <span>(left( M^{n},gright) )</span> of dimension <i>n</i> through an isometric embedding of <span>(left( M^{n},gright) )</span> into the Euclidean space <span>(left( R^{m},{overline{g}}right) )</span>, <span>(m&gt;n)</span>. For achieving this goal, we choose a constant unit vector <span>(overrightarrow{a})</span> on <span>(R^{m})</span> with its tangential component <span>(zeta )</span> and normal component <span>({overline{N}})</span>, and call <span>(zeta )</span> the KN-vector, <span>({overline{N}})</span> the KN-normal. We use a lower bound involving a smooth function <i>f</i> on <span>(M^{n})</span> on the integral of the Ricci curvature <span>(Ricleft( zeta ,zeta right) )</span> with respect to the <i>KN</i>-vector <span>(zeta )</span> to show that <span>(left( M^{n},g,zeta ,fright) )</span> is almost Ricci soliton, which is called the <i>KN</i>-almost Ricci soliton. The mean curvature vector <i>H</i>, gives a natural function <span>(varphi ={overline{g}}left( H,{overline{N}}right) )</span> on the <i>KN</i>-almost Ricci soliton <span>(left( M^{n},g,zeta ,fright) )</span> called <i>KN</i>-function. Then, we find a condition involving the <i>KN</i>-function <span>(varphi )</span> to show that an <i>n</i>-dimensional compact proper <i>KN</i>-almost Ricci soliton <span>(left( M^{n},g,zeta ,fright) )</span>, <span>(n&gt;2)</span>, is isometric to the sphere <span>(S^{n}(c))</span>. In this article, we also find conditions which make a compact <i>KN</i>-almost Ricci soliton <span>(left( M^{n},g,zeta ,fright) )</span> trivial. In first result in this direction, we show that a compact <i>n</i>-dimensional <i>KN</i>-almost Ricci soliton <span>(left( M^{n},g,zeta ,fright) )</span>, <span>(n&gt;2)</span>, with KN-function <span>(varphi )</span> and Ricci curvature in the direction of <span>(zeta )</span> bounded below by <span>(-(n-1)zeta left( varphi right) )</span> is either isometric to the sphere <span>(S^{n}(c))</span> or else it is a trivial Ricci soliton. Finally, we show that a compact <i>n</i>-dimensional <i>KN</i>-almost Ricci soliton <span>(left( M^{n},g,zeta ,fright) )</span>, <span>(n&gt;2)</span>, having scalar curvature <span>(tau )</span> and <i>KN</i>-function <span>(varphi )</span> satisfying <span>(tau varphi ge 0)</span> is necessarily a trivial Ricci soliton.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"29 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146027312","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Contact Process for the Spread of Knowledge","authors":"Nicolas Lanchier,&nbsp;Max Mercer,&nbsp;Hyunsik Yun","doi":"10.1007/s11040-025-09542-y","DOIUrl":"10.1007/s11040-025-09542-y","url":null,"abstract":"<div><p>This paper is concerned with a natural variant of the contact process modeling the spread of knowledge on the integer lattice. Each site is characterized by its knowledge, measured by a real number ranging from 0 = ignorant to 1 = omniscient. Neighbors interact at rate <span>(lambda )</span>, which results in both neighbors attempting to teach each other a fraction <span>(mu )</span> of their knowledge, and individuals die at rate one, which results in a new individual with no knowledge. Starting with a single omniscient site, our objective is to study whether the total amount of knowledge on the lattice converges to zero (extinction) or remains bounded away from zero (survival). The process dies out when <span>(lambda le lambda _c)</span> and/or <span>(mu = 0)</span>, where <span>(lambda _c)</span> denotes the critical value of the contact process. In contrast, we prove that, for all <span>(lambda &gt; lambda _c)</span>, there is a unique phase transition in the direction of <span>(mu )</span>, and for all <span>(mu &gt; 0)</span>, there is a unique phase transition in the direction of <span>(lambda )</span>. Our proof of survival relies on block constructions showing more generally convergence of the knowledge to infinity, while our proof of extinction relies on martingale techniques showing more generally an exponential decay of the knowledge.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"29 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146026928","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Complex Abstract Wiener Spaces","authors":"Tess J. van Leeuwen,&nbsp;Wioletta M. Ruszel","doi":"10.1007/s11040-025-09539-7","DOIUrl":"10.1007/s11040-025-09539-7","url":null,"abstract":"<div><p>Real abstract Wiener spaces (AWS) were originally defined by Gross using measurable norms, as a generalisation of the theory of advanced integral calculus in infinite dimensions as introduced by Cameron and Martin. In this paper we present a rigorous, complete and self-contained general framework for <span>(mathbb {K})</span>-AWS, where <span>(mathbb {K} in {mathbb {R},mathbb {C}})</span> using the language of characteristic functions instead of measurable norms. In particular, we will prove that <i>X</i> is a symmetric <i>H</i>-valued Gaussian field over <span>(mathbb {K})</span> iff the covariance function can be written in terms of some non-negative, self-adjoint trace class operator, and that the existence and uniqueness of <i>X</i> is equivalent to the <span>(mathbb {K})</span>-AWS. Finally we will relate the <span>(mathbb {C})</span>-AWS to the <span>(mathbb {R})</span>-AWS by way of a real structure, which is a real linear, complex anti-linear involution on a complex vector space. This allows for a commutative relation between the real and complex Gaussian fields and the real and complex abstract Wiener spaces. We will construct specific examples which fall under this framework like the complex Brownian motion, complex Feynman-Kac formula and complex fractional Gaussian fields.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"29 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145830994","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}