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Equivariant CR Yamabe problem 等变 CR 山边问题
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-07-08 DOI: 10.1007/s10231-024-01484-6
Pak Tung Ho
{"title":"Equivariant CR Yamabe problem","authors":"Pak Tung Ho","doi":"10.1007/s10231-024-01484-6","DOIUrl":"10.1007/s10231-024-01484-6","url":null,"abstract":"<div><p>As a generalization of the Yamabe problem, Hebey and Vaugon considered the equivariant Yamabe problem: for a subgroup <i>G</i> of the isometry group, find a <i>G</i>-invariant metric whose scalar curvature is constant in a given conformal class. In this paper, we introduce the equivariant CR Yamabe problem and prove some related results.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 1","pages":"289 - 306"},"PeriodicalIF":1.0,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573860","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}
引用次数: 0
The characteristic group of locally conformally product structures 局部保角积结构的特征群
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-07-02 DOI: 10.1007/s10231-024-01479-3
Brice Flamencourt
{"title":"The characteristic group of locally conformally product structures","authors":"Brice Flamencourt","doi":"10.1007/s10231-024-01479-3","DOIUrl":"10.1007/s10231-024-01479-3","url":null,"abstract":"<div><p>A compact manifold <i>M</i> together with a Riemannian metric <i>h</i> on its universal cover <span>(tilde{M})</span> for which <span>(pi _1(M))</span> acts by similarities is called a similarity structure. In the case where <span>(pi _1(M) not subset textrm{Isom}(tilde{M}, h))</span> and <span>((tilde{M}, h))</span> is reducible but not flat, this is a Locally Conformally Product (LCP) structure. The so-called characteristic group of these manifolds, which is a connected abelian Lie group, is the key to understand how they are built. We focus in this paper on the case where this group is simply connected, and give a description of the corresponding LCP structures. It appears that they are quotients of trivial <span>(mathbb {R}^p)</span>-principal bundles over simply-connected manifolds by certain discrete subgroups of automorphisms. We prove that, conversely, it is always possible to endow such quotients with an LCP structure.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 1","pages":"189 - 211"},"PeriodicalIF":1.0,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141527549","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}
引用次数: 0
Domination of nonlinear semigroups generated by regular, local Dirichlet forms
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-07-02 DOI: 10.1007/s10231-024-01478-4
Ralph Chill, Burkhard Claus
{"title":"Domination of nonlinear semigroups generated by regular, local Dirichlet forms","authors":"Ralph Chill,&nbsp;Burkhard Claus","doi":"10.1007/s10231-024-01478-4","DOIUrl":"10.1007/s10231-024-01478-4","url":null,"abstract":"<div><p>In this article we study perturbations of local, nonlinear Dirichlet forms on arbitrary topological measure spaces. As a main result, we show that the semigroup generated by a local, regular, nonlinear Dirichlet form <span>({mathcal {E}})</span> dominates the semigroup generated by another local functional <span>({mathcal {F}})</span> if, and only if, <span>({mathcal {F}})</span> is a specific zero order perturbation of <span>({mathcal {E}})</span>. On the way, we prove a nonlinear version of the Riesz–Markov representation theorem, we define an abstract boundary of a topological measure space, and apply the notion of nonlinear capacity. The main result helps to classify the perturbations that lie between Neumann and Dirichlet boundary conditions.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 1","pages":"163 - 188"},"PeriodicalIF":1.0,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-024-01478-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143423065","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}
引用次数: 0
Heights and transcendence of p-adic continued fractions p-adic 續分數的高度和超越性
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-07-02 DOI: 10.1007/s10231-024-01476-6
Ignazio Longhi, Nadir Murru, Francesco M. Saettone
{"title":"Heights and transcendence of p-adic continued fractions","authors":"Ignazio Longhi,&nbsp;Nadir Murru,&nbsp;Francesco M. Saettone","doi":"10.1007/s10231-024-01476-6","DOIUrl":"10.1007/s10231-024-01476-6","url":null,"abstract":"<div><p>Special kinds of continued fractions have been proved to converge to transcendental real numbers by means of the celebrated Subspace Theorem. In this paper we study the analogous <i>p</i>–adic problem. More specifically, we deal with Browkin <i>p</i>–adic continued fractions. First we give some new remarks about the Browkin algorithm in terms of a <i>p</i>–adic Euclidean algorithm. Then, we focus on the heights of some <i>p</i>–adic numbers having a periodic <i>p</i>–adic continued fraction expansion and we obtain some upper bounds. Finally, we exploit these results, together with <i>p</i>–adic Roth-like results, in order to prove the transcendence of three families of <i>p</i>–adic continued fractions.\u0000</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 1","pages":"129 - 145"},"PeriodicalIF":1.0,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141527550","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}
引用次数: 0
A Hilbert–Mumford criterion for polystability for actions of real reductive Lie groups 实还原李群作用多稳性的希尔伯特-蒙福德准则
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-07-02 DOI: 10.1007/s10231-024-01480-w
Leonardo Biliotti, Oluwagbenga Joshua Windare
{"title":"A Hilbert–Mumford criterion for polystability for actions of real reductive Lie groups","authors":"Leonardo Biliotti,&nbsp;Oluwagbenga Joshua Windare","doi":"10.1007/s10231-024-01480-w","DOIUrl":"10.1007/s10231-024-01480-w","url":null,"abstract":"<div><p>We study a Hilbert–Mumford criterion for polystablility associated with an action of a real reductive Lie group <i>G</i> on a real submanifold <i>X</i> of a Kähler manifold <i>Z</i>. Suppose the action of a compact Lie group with Lie algebra <span>(mathfrak {u})</span> extends holomorphically to an action of the complexified group <span>(U^{mathbb {C}})</span> and that the <i>U</i>-action on <i>Z</i> is Hamiltonian. If <span>(Gsubset U^{mathbb {C}})</span> is compatible, there is a corresponding gradient map <span>(mu _mathfrak {p}: Xrightarrow mathfrak {p})</span>, where <span>(mathfrak {g}= mathfrak {k}oplus mathfrak {p})</span> is a Cartan decomposition of the Lie algebra of <i>G</i>. Under some mild restrictions on the <i>G</i>-action on <i>X</i>,  we characterize which <i>G</i>-orbits in <i>X</i> intersect <span>(mu _mathfrak {p}^{-1}(0))</span> in terms of the maximal weight functions, which we viewed as a collection of maps defined on the boundary at infinity (<span>(partial _infty G/K)</span>) of the symmetric space <i>G</i>/<i>K</i>. We also establish the Hilbert–Mumford criterion for polystability of the action of <i>G</i> on measures.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 1","pages":"213 - 229"},"PeriodicalIF":1.0,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-024-01480-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141527514","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}
引用次数: 0
Partial separability and symplectic-Haantjes manifolds 部分可分性和交映-Haantjes 流形
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-07-02 DOI: 10.1007/s10231-024-01462-y
Daniel Reyes, Piergiulio Tempesta, Giorgio Tondo
{"title":"Partial separability and symplectic-Haantjes manifolds","authors":"Daniel Reyes,&nbsp;Piergiulio Tempesta,&nbsp;Giorgio Tondo","doi":"10.1007/s10231-024-01462-y","DOIUrl":"10.1007/s10231-024-01462-y","url":null,"abstract":"<div><p>A theory of partial separability for classical Hamiltonian systems is proposed in the context of Haantjes geometry. As a general result, we show that the knowledge of a non-semisimple symplectic-Haantjes manifold for a given Hamiltonian system is sufficient to construct sets of coordinates (called Darboux-Haantjes coordinates) that allow both the partial separability of the associated Hamilton-Jacobi equations and the block-diagonalization of the operators of the corresponding Haantjes algebra. We also introduce a novel class of Hamiltonian systems, characterized by the existence of a generalized Stäckel matrix, which by construction are partially separable. They widely generalize the known families of partially separable Hamiltonian systems. The new systems can be described in terms of semisimple but non-maximal-rank symplectic-Haantjes manifolds.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"203 6","pages":"2677 - 2710"},"PeriodicalIF":1.0,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-024-01462-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141527548","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}
引用次数: 0
Quasilinear elliptic problem in anisotropic Orlicz–Sobolev space on unbounded domain 无界域上各向异性 Orlicz-Sobolev 空间中的准线性椭圆问题
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-06-29 DOI: 10.1007/s10231-024-01477-5
Karol Wroński
{"title":"Quasilinear elliptic problem in anisotropic Orlicz–Sobolev space on unbounded domain","authors":"Karol Wroński","doi":"10.1007/s10231-024-01477-5","DOIUrl":"10.1007/s10231-024-01477-5","url":null,"abstract":"<div><p>We study a quasilinear elliptic problem <span>(-text {div} (nabla Phi (nabla u))+V(x)N'(u)=f(u))</span> with anisotropic convex function <span>(Phi )</span> on the whole <span>(mathbb {R}^n)</span>. To prove existence of a nontrivial weak solution we use the mountain pass theorem for a functional defined on anisotropic Orlicz–Sobolev space <span>({{{,mathrm{textbf{W}},}}^1}{{,mathrm{textbf{L}},}}^{{Phi }} (mathbb {R}^n))</span>. As the domain is unbounded we need to use Lions type lemma formulated for Young functions. Our assumptions broaden the class of considered functions <span>(Phi )</span> so our result generalizes earlier analogous results proved in isotropic setting.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 1","pages":"147 - 161"},"PeriodicalIF":1.0,"publicationDate":"2024-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-024-01477-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141496166","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}
引用次数: 0
General birationality and hyperelliptic theta divisors
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-06-25 DOI: 10.1007/s10231-024-01473-9
Fabrizio Catanese
{"title":"General birationality and hyperelliptic theta divisors","authors":"Fabrizio Catanese","doi":"10.1007/s10231-024-01473-9","DOIUrl":"10.1007/s10231-024-01473-9","url":null,"abstract":"<div><p>We first state a condition ensuring that having a birational map onto the image is an open property for families of irreducible normal non uniruled varieties. We give then some criteria to ensure general birationality for a family of rational maps, via specializations. Among the applications is a new proof of the main result of Catanese and Cesarano (Electron Res Arch 29(6):4315–4325, 2021) that, for a general pair (<i>A</i>, <i>X</i>) of an (ample) Hypersurface <i>X</i> in an Abelian Variety <i>A</i>, the canonical map <span>(Phi _X)</span> of <i>X</i> is birational onto its image if the polarization given by <i>X</i> is not principal. The proof is also based on a careful study of the Theta divisors of the Jacobians of Hyperelliptic curves, and some related geometrical constructions. We investigate these here also in view of their beauty and of their independent interest, as they lead to a description of the rings of Hyperelliptic theta functions.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 1","pages":"53 - 71"},"PeriodicalIF":1.0,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-024-01473-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143423273","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}
引用次数: 0
Reconstruction of the initial condition in parabolic equations with Log-Lipschitz coefficients
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-06-22 DOI: 10.1007/s10231-024-01475-7
Daniele Del Santo, Martino Prizzi
{"title":"Reconstruction of the initial condition in parabolic equations with Log-Lipschitz coefficients","authors":"Daniele Del Santo,&nbsp;Martino Prizzi","doi":"10.1007/s10231-024-01475-7","DOIUrl":"10.1007/s10231-024-01475-7","url":null,"abstract":"<div><p>We consider a parabolic equation whose coefficients are Log-Lipschitz continuous in <i>t</i> and Lipschitz continuous in <i>x</i>. Combining a recent conditional stability result with a well posed variational problem, we reconstruct the initial condition of an unknown solution from a rough measurement at the final time.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 1","pages":"117 - 127"},"PeriodicalIF":1.0,"publicationDate":"2024-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-024-01475-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143423045","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}
引用次数: 0
Non-radial ground state solutions for fractional Schrödinger–Poisson systems in (mathbb {R}^{2}) 分数薛定谔-泊松系统在 $$mathbb {R}^{2}$ 中的非径向基态解
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-06-20 DOI: 10.1007/s10231-024-01470-y
Guofeng Che, Juntao Sun, Tsung-Fang Wu
{"title":"Non-radial ground state solutions for fractional Schrödinger–Poisson systems in (mathbb {R}^{2})","authors":"Guofeng Che,&nbsp;Juntao Sun,&nbsp;Tsung-Fang Wu","doi":"10.1007/s10231-024-01470-y","DOIUrl":"10.1007/s10231-024-01470-y","url":null,"abstract":"<div><p>In this paper, we study the fractional Schrödinger–Poisson system with a general nonlinearity as follows: </p><div><div><span>$$begin{aligned} left{ begin{array}{ll} (-Delta )^{s}u+u+ l(x)phi u=f(u) &amp;{} text { in }mathbb {R}^{2}, (-Delta )^{t}phi =l(x)u^{2} &amp;{} text { in }mathbb {R}^{2}, end{array} right. end{aligned}$$</span></div></div><p>where <span>(frac{1}{2}&lt;tle s&lt;1)</span>, the potential <span>(lin C(mathbb {R}^{2},mathbb {R}^{+}))</span> and <span>(fin C(mathbb {R},mathbb {R}))</span> does not require the classical (AR)-condition. When <span>(l(x)equiv mu &gt;0)</span> is a parameter, by establishing new estimates for the fractional Laplacian, we find two positive solutions, depending on the range of <span>(mu )</span>. As a result, a positive ground state solution with negative energy exists for the non-autonomous system without any symmetry on <i>l</i>(<i>x</i>). When <i>l</i>(<i>x</i>) is radially symmetric, we show that the symmetry breaking phenomenon can occur, and that a non-radial ground state solution with negative energy exists. Furthermore, under additional assumptions on <i>l</i>(<i>x</i>), three positive solutions are found. The intrinsic differences between the planar SP system and the planar fSP system are analyzed.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"203 6","pages":"2863 - 2888"},"PeriodicalIF":1.0,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141500609","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}
引用次数: 0
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