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New eigenvalue pinching results for Euclidean domains 欧氏域的新特征值捏合结果
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-07-14 DOI: 10.1007/s10231-024-01485-5
Julien Roth, Abhitosh Upadhyay
{"title":"New eigenvalue pinching results for Euclidean domains","authors":"Julien Roth,&nbsp;Abhitosh Upadhyay","doi":"10.1007/s10231-024-01485-5","DOIUrl":"10.1007/s10231-024-01485-5","url":null,"abstract":"<div><p>We prove stability results associated with sharp eigenvalue upper bounds for several operators on embedded hypersurfaces and boundary problems on smooth domains of the Euclidean space. These upper bounds involve isoperimetric ratio and mean curvature terms. The stability results derive from a general pinching result for the moment of inertia. \u0000</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 1","pages":"307 - 326"},"PeriodicalIF":1.0,"publicationDate":"2024-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141650394","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
Gradient continuity for the parabolic ((1,,p))-Laplace equation under the subcritical case 次临界情况下抛物$$(1,,p)$$ -拉普拉斯方程的梯度连续性
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-07-12 DOI: 10.1007/s10231-024-01483-7
Shuntaro Tsubouchi
{"title":"Gradient continuity for the parabolic ((1,,p))-Laplace equation under the subcritical case","authors":"Shuntaro Tsubouchi","doi":"10.1007/s10231-024-01483-7","DOIUrl":"10.1007/s10231-024-01483-7","url":null,"abstract":"<div><p>This paper is concerned with the gradient continuity for the parabolic <span>((1,,p))</span>-Laplace equation. In the supercritical case <span>(frac{2n}{n+2}&lt;p&lt;infty )</span>, where <span>(nge 2)</span> denotes the space dimension, this gradient regularity result has been proved recently by the author. In this paper, we would like to prove that the same regularity holds even for the subcritical case <span>(1&lt;ple frac{2n}{n+2})</span> with <span>(nge 3)</span>, on the condition that a weak solution admits the <span>(L^{s})</span>-integrability with <span>(s&gt;frac{n(2-p)}{p})</span>. The gradient continuity is proved, similarly to the supercritical case, once the local gradient bounds of solutions are verified. Hence, this paper mainly aims to show the local boundedness of a solution and its gradient by Moser’s iteration. The proof is completed by considering a parabolic approximate problem, verifying a comparison principle, and showing a priori gradient estimates of a bounded weak solution to the relaxed equation.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 1","pages":"261 - 287"},"PeriodicalIF":1.0,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-024-01483-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141614944","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
Weak Poissonian correlations 弱泊松相关性
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-07-10 DOI: 10.1007/s10231-024-01463-x
Manuel Hauke, Agamemnon Zafeiropoulos
{"title":"Weak Poissonian correlations","authors":"Manuel Hauke,&nbsp;Agamemnon Zafeiropoulos","doi":"10.1007/s10231-024-01463-x","DOIUrl":"10.1007/s10231-024-01463-x","url":null,"abstract":"<div><p>We examine a property of sequences called Poissonian pair correlations with parameter <span>(0leqslant beta leqslant 1)</span> (abbreviated as <span>(beta)</span>-PPC). We prove that when <span>(beta &lt;1,)</span> the property of <span>(beta)</span>-PPC, also known as weak Poissonian correlations, can be detected at the behaviour of sequences at small scales, and show that this does not happen for the classical notion of PPC, that is, when <span>(beta = 1)</span>. Furthermore, we show that whenever <span>(0leqslant alpha &lt; beta leqslant 1)</span>, <span>(beta)</span>-PPC is stronger than <span>(alpha)</span>-PPC. We also include a discussion on weak Poissonian correlations of higher orders, showing that for <span>(beta &lt; 1)</span>, Poissonian <span>(beta)</span>-correlations of order <span>(k+1)</span> imply Poissonian <span>(beta)</span>-correlations of <i>k</i>-th order with the same parameter <span>(beta)</span>.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"203 6","pages":"2711 - 2740"},"PeriodicalIF":1.0,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-024-01463-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141661866","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
Endpoint estimates for riesz transform on manifolds with ends 有端流形上 riesz 变换的端点估计
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-07-09 DOI: 10.1007/s10231-024-01482-8
Dangyang He
{"title":"Endpoint estimates for riesz transform on manifolds with ends","authors":"Dangyang He","doi":"10.1007/s10231-024-01482-8","DOIUrl":"10.1007/s10231-024-01482-8","url":null,"abstract":"<div><p>We consider a class of non-doubling manifolds <span>(mathcal {M})</span> consisting of finite many “Euclidean” ends, where the Euclidean dimensions at infinity are not necessarily all the same. In [17], Hassell and Sikora proved that the Riesz transform on <span>(mathcal {M})</span> is of weak type (1, 1), bounded on <span>(L^{p})</span> if and only if <span>(1&lt;p&lt;n_*)</span>, where <span>(n_* = min _k n_k)</span>. In this note, we complete the picture by giving an endpoint estimate: Riesz transform is bounded on Lorentz space <span>(L^{n_*,1})</span> and unbounded from <span>(L^{n_*,p}rightarrow L^{n_*,q})</span> for all <span>(1&lt;p&lt;infty )</span> and <span>(ple qle infty )</span>.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 1","pages":"245 - 259"},"PeriodicalIF":1.0,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-024-01482-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141665313","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
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
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