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Chern-kuiper’s inequalities Chern-kuiper 不等式
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-08-04 DOI: 10.1007/s10231-024-01492-6
Diego Guajardo
{"title":"Chern-kuiper’s inequalities","authors":"Diego Guajardo","doi":"10.1007/s10231-024-01492-6","DOIUrl":"10.1007/s10231-024-01492-6","url":null,"abstract":"<div><p>Given a Euclidean submanifold <span>(g:M^{n}rightarrow {mathbb {R}}^{n+p})</span>, Chern and Kuiper provided inequalities between <span>(mu )</span> and <span>(nu _g)</span>, the ranks of the nullity of <span>(M^n)</span> and the relative nullity of <i>g</i> respectively. Namely, they prove that </p><div><div><span>$$begin{aligned} nu _gle mu le nu _g+p. end{aligned}$$</span></div><div>\u0000 (1)\u0000 </div></div><p>In this work, we study the submanifolds with <span>(nu _gne mu )</span>. More precisely, we characterize locally the ones with <span>(0ne (mu -nu _g)in {p,p-1,p-2})</span> under the hypothesis of <span>(nu _gle n-p-1)</span>.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 2","pages":"477 - 488"},"PeriodicalIF":1.0,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141929882","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
Moser–Trudinger inequalities: from local to global Moser-Trudinger不平等：从地方到全球
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-07-30 DOI: 10.1007/s10231-024-01481-9
Luigi Fontana, Carlo Morpurgo, Liuyu Qin
{"title":"Moser–Trudinger inequalities: from local to global","authors":"Luigi Fontana,&nbsp;Carlo Morpurgo,&nbsp;Liuyu Qin","doi":"10.1007/s10231-024-01481-9","DOIUrl":"10.1007/s10231-024-01481-9","url":null,"abstract":"<div><p>Given a general complete Riemannian manifold <i>M</i>, we introduce the concept of “local Moser–Trudinger inequality on <span>(W^{1,n}(M))</span>”. We show how the validity of the Moser–Trudinger inequality can be extended from a local to a global scale under additional assumptions: either by assuming the validity of the Poincaré inequality, or by imposing a stronger norm condition. We apply these results to Hadamard manifolds. The technique is general enough to be applicable also in sub-Riemannian settings, such as the Heisenberg group.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 1","pages":"231 - 243"},"PeriodicalIF":1.0,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143422993","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
Some counterexamples to Alt–Caffarelli–Friedman monotonicity formulas in Carnot groups 卡诺群中al - caffarelli - friedman单调公式的一些反例
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-07-29 DOI: 10.1007/s10231-024-01490-8
Fausto Ferrari, Davide Giovagnoli
{"title":"Some counterexamples to Alt–Caffarelli–Friedman monotonicity formulas in Carnot groups","authors":"Fausto Ferrari,&nbsp;Davide Giovagnoli","doi":"10.1007/s10231-024-01490-8","DOIUrl":"10.1007/s10231-024-01490-8","url":null,"abstract":"<div><p>In this paper we continue the analysis of an Alt–Caffarelli–Friedman (ACF) monotonicity formula in Carnot groups of step <span>(s &gt;1)</span> confirming the existence of counterexamples to the monotone increasing behavior. In particular, we provide a sufficient condition that implies the existence of some counterexamples to the monotone increasing behavior of the ACF formula in Carnot groups. The main tool is based on the lack of orthogonality of harmonic polynomials in Carnot groups. This paper generalizes the results proved in Ferrari and Forcillo (Atti Accad Naz Lincei Rend Lincei Mat Appl 34(2):295–306, 2023).</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 2","pages":"427 - 445"},"PeriodicalIF":1.0,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-024-01490-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143688393","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
Inequalities for eigenvalues of the bi-drifting Laplacian on bounded domains in complete noncompact Riemannian manifolds and related results 完全非紧密黎曼流形有界域上的双漂移拉普拉奇特征值不等式及相关结果
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-07-26 DOI: 10.1007/s10231-024-01486-4
Yue He, Shiyun Pu
{"title":"Inequalities for eigenvalues of the bi-drifting Laplacian on bounded domains in complete noncompact Riemannian manifolds and related results","authors":"Yue He,&nbsp;Shiyun Pu","doi":"10.1007/s10231-024-01486-4","DOIUrl":"10.1007/s10231-024-01486-4","url":null,"abstract":"<div><p>In this paper, we investigate the universal inequalities for eigenvalues of the bi-drifting Laplacian on bounded domains in an <i>n</i>-dimensional complete noncompact simply connected Riemannian manifold with its sectional curvature satisfying certain pinching conditions, in a Gaussian shrinking soliton, and in a cigar metric measure space, respectively. By using some analytic inequalities and geometric inequalities, we establish some new universal inequalities which are different from those already present in the literature, such as Yanli Li and Feng Du’s [Arch Math (Basel) 109(6):591–598, 2017], Feng Du et al.’s [Z Angew Math Phys 66(3):703–726, (2015)] and Xinyang Li, Xin Xiong and Lingzhong Zeng’s [J Geom Phys 145:103472, (2019)].\u0000</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 1","pages":"327 - 358"},"PeriodicalIF":1.0,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141801810","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
Necessary and sufficient conditions on entire solvability for real ((n-1)) Monge–Ampère equation 实$$(n-1)$$蒙日-安培方程整体可解性的必要条件和充分条件
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-07-26 DOI: 10.1007/s10231-024-01491-7
Feida Jiang, Jingwen Ji, Mengni Li
{"title":"Necessary and sufficient conditions on entire solvability for real ((n-1)) Monge–Ampère equation","authors":"Feida Jiang,&nbsp;Jingwen Ji,&nbsp;Mengni Li","doi":"10.1007/s10231-024-01491-7","DOIUrl":"10.1007/s10231-024-01491-7","url":null,"abstract":"<div><p>In this paper, we establish a necessary and sufficient condition on solvability for the entire sub-solutions to the real <span>((n-1))</span> Monge–Ampère equation <span>(textrm{det} ^{1/n}(Delta uI-D^2 u)=b(x)f(u))</span> in <span>({mathbb {R}}^n)</span>, which can be regarded as a generalized Keller–Osserman condition. When <i>b</i> is spherically symmetric, we establish the existence of entire large solutions in radial sense. When <i>b</i> is non-spherically symmetric, we obtain the existence of entire bounded solutions using the standard sub- and super-solution method. Finally, the nonexistence results are extended to Hessian quotient equations for a general function <i>b</i> when <i>f</i> are polynomial and exponential functions, respectively.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 2","pages":"447 - 476"},"PeriodicalIF":1.0,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141799517","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
Construction of semi-orthogonal wavelet frames on locally compact abelian groups 在局部紧凑无性群上构建半正交小波框架
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-07-21 DOI: 10.1007/s10231-024-01488-2
Satyapriya, Raj Kumar, Firdous A. Shah
{"title":"Construction of semi-orthogonal wavelet frames on locally compact abelian groups","authors":"Satyapriya,&nbsp;Raj Kumar,&nbsp;Firdous A. Shah","doi":"10.1007/s10231-024-01488-2","DOIUrl":"10.1007/s10231-024-01488-2","url":null,"abstract":"<div><p>Keeping in view the recent developments of wavelets on locally compact Abelian groups (LCA) along with the applicability of the unifying structure of LCA groups, we present an explicit and efficient method for the construction of wavelet frames of arbitrary dilations on LCA groups. The method is exhibited via several illustrative examples.\u0000</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 1","pages":"387 - 406"},"PeriodicalIF":1.0,"publicationDate":"2024-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141742594","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
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
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