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Complex Dirac structures with constant real index on flag manifolds 旗流形上具有恒定实指数的复狄拉克结构
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-10-27 DOI: 10.1007/s10231-023-01394-z
Cristian Ortiz, Carlos Varea
{"title":"Complex Dirac structures with constant real index on flag manifolds","authors":"Cristian Ortiz,&nbsp;Carlos Varea","doi":"10.1007/s10231-023-01394-z","DOIUrl":"10.1007/s10231-023-01394-z","url":null,"abstract":"<div><p>In this paper we describe all invariant complex Dirac structures with constant real index on a maximal flag manifold in terms of the roots of the Lie algebra which defines the flag manifold. We also completely classify these structures under the action of <i>B</i>-transformations. \u0000</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136317069","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
Non-degeneracy of the multi-bump solutions to the Brezis-Nirenberg problem 布雷齐斯-尼伦堡问题多凸点解的非退化性
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-10-27 DOI: 10.1007/s10231-023-01395-y
Haixia Chen, Chunhua Wang, Huafei Xie, Yang Zhou
{"title":"Non-degeneracy of the multi-bump solutions to the Brezis-Nirenberg problem","authors":"Haixia Chen,&nbsp;Chunhua Wang,&nbsp;Huafei Xie,&nbsp;Yang Zhou","doi":"10.1007/s10231-023-01395-y","DOIUrl":"10.1007/s10231-023-01395-y","url":null,"abstract":"<div><p>We revisit the well-known Brezis-Nirenberg problem </p><div><div><span>$$begin{aligned} {left{ begin{array}{ll} -Delta u= u^{frac{N+2}{N-2}}+varepsilon u, &amp;{}{{text {in}}~Omega }, u&gt;0, &amp;{}{{text {in}}~Omega }, u=0, &amp;{}{text {on}~partial Omega }, end{array}right. } end{aligned}$$</span></div></div><p>where <span>(varepsilon &gt;0)</span> and <span>(Omega subset mathbb {R}^N)</span> are a smooth bounded domain with <span>(Nge 3)</span>. The existence of multi-bump solutions to above problem for small parameter <span>(varepsilon &gt;0)</span> was obtained by Musso and Pistoia (Indiana Univ Math J 51:541–579, 2002). However, to our knowledge, whether the multi-bump solutions are non-degenerate that is open. Here, we give some straightforward answer on this question under some suitable assumptions for the Green’s function of <span>(-Delta )</span> in <span>(Omega )</span>, which enriches the qualitative analysis on the solutions of Brezis-Nirenberg problem and can be viewed as a generalization of Grossi (Nonlinear Differ Equ Appl 12:227–241, 2005) where the non-degeneracy of a single-bump solution has been proved. And the main idea is the blow-up analysis based on the local Pohozaev identities.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136317359","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
Hopf type theorems for surfaces in the de Sitter–Schwarzschild and Reissner–Nordstrom manifolds 德西特-施瓦兹柴尔德流形和赖斯纳-诺德斯特罗姆流形中曲面的霍普夫型定理
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-10-27 DOI: 10.1007/s10231-023-01384-1
Hilário Alencar, Gregório Silva Neto
{"title":"Hopf type theorems for surfaces in the de Sitter–Schwarzschild and Reissner–Nordstrom manifolds","authors":"Hilário Alencar,&nbsp;Gregório Silva Neto","doi":"10.1007/s10231-023-01384-1","DOIUrl":"10.1007/s10231-023-01384-1","url":null,"abstract":"<div><p>In 1951, Hopf proved that the only surfaces, homeomorphic to the sphere, with constant mean curvature in Euclidean space are the round (geometrical) spheres. These results were generalized by S. S. Chern and then by Eschenburg and Tribuzy for surfaces homeomorphic to the sphere in Riemannian manifolds with constant sectional curvature whose mean curvature function satisfies some bound on its differential. In this paper, we extend these results for surfaces in a wide class of warped product manifolds, which includes, besides the classical space forms of constant sectional curvature, the de Sitter–Schwarzschild manifolds and the Reissner–Nordstrom manifolds, which are time slices of solutions of the Einstein field equations of general relativity.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136235858","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
Compactifications of indefinite 3-Sasaki structures and their quaternionic Kähler quotients 不定3-Sasaki结构的紧凑化及其四元凯勒商数
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-10-25 DOI: 10.1007/s10231-023-01385-0
A. Rod Gover, Katharina Neusser, Travis Willse
{"title":"Compactifications of indefinite 3-Sasaki structures and their quaternionic Kähler quotients","authors":"A. Rod Gover,&nbsp;Katharina Neusser,&nbsp;Travis Willse","doi":"10.1007/s10231-023-01385-0","DOIUrl":"10.1007/s10231-023-01385-0","url":null,"abstract":"<div><p>We show that 3-Sasaki structures admit a natural description in terms of projective differential geometry. First we establish that a 3-Sasaki structure may be understood as a projective structure whose tractor connection admits a holonomy reduction, satisfying a particular non-vanishing condition, to the (possibly indefinite) unitary quaternionic group <span>({text {Sp}}(p,q))</span>. Moreover, we show that, if a holonomy reduction to <span>({text {Sp}}(p,q))</span> of the tractor connection of a projective structure does not satisfy this condition, then it decomposes the underlying manifold into a disjoint union of strata including open manifolds with (indefinite) 3-Sasaki structures and a closed separating hypersurface at infinity with respect to the 3-Sasaki metrics. It is shown that the latter hypersurface inherits a Biquard–Fefferman conformal structure, which thus (locally) fibers over a quaternionic contact structure, and which in turn compactifies the natural quaternionic Kähler quotients of the 3-Sasaki structures on the open manifolds. As an application, we describe the projective compactification of (suitably) complete, non-compact (indefinite) 3-Sasaki manifolds and recover Biquard’s notion of asymptotically hyperbolic quaternionic Kähler metrics.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-023-01385-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135113405","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
Variations on average character degrees and solvability 平均字符度和可解性的变化
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-10-24 DOI: 10.1007/s10231-023-01393-0
Neda Ahanjideh, Zeinab Akhlaghi, Kamal Aziziheris
{"title":"Variations on average character degrees and solvability","authors":"Neda Ahanjideh,&nbsp;Zeinab Akhlaghi,&nbsp;Kamal Aziziheris","doi":"10.1007/s10231-023-01393-0","DOIUrl":"10.1007/s10231-023-01393-0","url":null,"abstract":"<div><p>Let <i>G</i> be a finite group, <span>(mathbb {F})</span> be one of the fields <span>(mathbb {Q},mathbb {R})</span> or <span>(mathbb {C})</span>, and <i>N</i> be a non-trivial normal subgroup of <i>G</i>. Let <span>({textrm{acd}}^{*}_{{mathbb {F}}}(G))</span> and <span>({textrm{acd}}_{{mathbb {F}}, textrm{even}}(G|N))</span> be the average degree of all non-linear <span>(mathbb {F})</span>-valued irreducible characters of <i>G</i> and of even degree <span>(mathbb {F})</span>-valued irreducible characters of <i>G</i> whose kernels do not contain <i>N</i>, respectively. We assume the average of an empty set is zero for more convenience. In this paper we prove that if <span>(textrm{acd}^*_{mathbb {Q}}(G)&lt; 9/2)</span> or <span>(0&lt;textrm{acd}_{mathbb {Q},textrm{even}}(G|N)&lt;4)</span>, then <i>G</i> is solvable. Moreover, setting <span>(mathbb {F} in {mathbb {R},mathbb {C}})</span>, we obtain the solvability of <i>G</i> by assuming <span>({textrm{acd}}^{*}_{{mathbb {F}}}(G)&lt;29/8)</span> or <span>(0&lt;{textrm{acd}}_{{mathbb {F}}, textrm{even}}(G|N)&lt;7/2)</span>, and we conclude the solvability of <i>N</i> when <span>(0&lt;{textrm{acd}}_{{mathbb {F}}, textrm{even}}(G|N)&lt;18/5)</span>. Replacing <i>N</i> by <i>G</i> in <span>({textrm{acd}}_{{mathbb {F}}, textrm{even}}(G|N))</span> gives us an extended form of a result by Moreto and Nguyen. Examples are given to show that all the bounds are sharp.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135266466","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
Harmonic almost complex structures on almost abelian Lie groups and solvmanifolds 几乎无差别李群和溶点上的谐波近复结构
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-10-24 DOI: 10.1007/s10231-023-01392-1
Adrián Andrada, Alejandro Tolcachier
{"title":"Harmonic almost complex structures on almost abelian Lie groups and solvmanifolds","authors":"Adrián Andrada,&nbsp;Alejandro Tolcachier","doi":"10.1007/s10231-023-01392-1","DOIUrl":"10.1007/s10231-023-01392-1","url":null,"abstract":"<div><p>An almost abelian Lie group is a solvable Lie group with a codimension one normal abelian subgroup. We characterize almost Hermitian structures on almost abelian Lie groups where the almost complex structure is harmonic with respect to the Hermitian metric. Also, we adapt the Gray–Hervella classification of almost Hermitian structures to the family of almost abelian Lie groups. We provide several examples of harmonic almost complex structures in different Gray–Hervella classes on some associated compact almost abelian solvmanifolds.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135267861","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
End-point norm estimates for Cesàro and Copson operators Cesàro 和 Copson 算子的端点规范估计值
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-10-15 DOI: 10.1007/s10231-023-01390-3
Sorina Barza, Bizuneh M. Demissie, Gord Sinnamon
{"title":"End-point norm estimates for Cesàro and Copson operators","authors":"Sorina Barza,&nbsp;Bizuneh M. Demissie,&nbsp;Gord Sinnamon","doi":"10.1007/s10231-023-01390-3","DOIUrl":"10.1007/s10231-023-01390-3","url":null,"abstract":"<div><p>For a large class of operators acting between weighted <span>(ell ^infty)</span> spaces, exact formulas are given for their norms and the norms of their restrictions to the cones of nonnegative sequences; nonnegative, nonincreasing sequences; and nonnegative, nondecreasing sequences. The weights involved are arbitrary nonnegative sequences and may differ in the domain and codomain spaces. The results are applied to the Cesàro and Copson operators, giving their norms and their distances to the identity operator on the whole space and on the cones. Simplifications of these formulas are derived in the case of these operators acting on power-weighted <span>(ell ^infty)</span>. As an application, best constants are given for inequalities relating the weighted <span>(ell ^infty)</span> norms of the Cesàro and Copson operators both for general weights and for power weights.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136184735","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
Analysis of a system modeling the interaction between the motion of piston-spring and a viscous gas 活塞弹簧运动与粘性气体相互作用模型系统分析
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-10-13 DOI: 10.1007/s10231-023-01386-z
Sabrine Chebbi, Václav Mácha, Šárka Nečasová
{"title":"Analysis of a system modeling the interaction between the motion of piston-spring and a viscous gas","authors":"Sabrine Chebbi,&nbsp;Václav Mácha,&nbsp;Šárka Nečasová","doi":"10.1007/s10231-023-01386-z","DOIUrl":"10.1007/s10231-023-01386-z","url":null,"abstract":"<div><p>We are concerned with a one-dimensional flow of a compressible fluid which may be seen as a simplification of the flow of fluid in a long thin pipe. We assume that the pipe is on one side ended by a spring. The other side of the pipe is let open—there we assume either inflow or outflow boundary conditions. Such situation can be understood as a toy model for human lungs. We tackle the question of uniqueness and existence of a strong solution for a system modeling the above process, special emphasis is laid upon the estimate of the maximal time of existence.\u0000</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135855344","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
Sectional nonassociativity of metrized algebras 元化代数的截面非可共性
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-10-08 DOI: 10.1007/s10231-023-01372-5
Daniel J. F. Fox
{"title":"Sectional nonassociativity of metrized algebras","authors":"Daniel J. F. Fox","doi":"10.1007/s10231-023-01372-5","DOIUrl":"10.1007/s10231-023-01372-5","url":null,"abstract":"<div><p>The sectional nonassociativity of a metrized (not necessarily associative or unital) algebra is defined analogously to the sectional curvature of a pseudo-Riemannian metric, with the associator in place of the Levi-Civita covariant derivative. For commutative real algebras nonnegative sectional nonassociativity is usually called the Norton inequality, while a sharp upper bound on the sectional nonassociativity of the Jordan algebra of Hermitian matrices over a real Hurwitz algebra is closely related to the Böttcher–Wenzel-Chern-do Carmo-Kobayashi inequality. These and other basic examples are explained, and there are described some consequences of bounds on sectional nonassociativity for commutative algebras. A technical point of interest is that the results work over the octonions as well as the associative Hurwitz algebras.\u0000</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-023-01372-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135197590","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
Orbital stability of solitary waves for a two-component Novikov system 双分量诺维科夫系统孤波的轨道稳定性
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-10-08 DOI: 10.1007/s10231-023-01391-2
Rudong Zheng
{"title":"Orbital stability of solitary waves for a two-component Novikov system","authors":"Rudong Zheng","doi":"10.1007/s10231-023-01391-2","DOIUrl":"10.1007/s10231-023-01391-2","url":null,"abstract":"<div><p>We consider solitary wave solutions of a two-component Novikov system, which is a coupled Camassa-Holm type system with cubic nonlinearity. Inspired by the methods established by Constantin and Strauss in [6, 7], we prove that the smooth solitary waves and non-smooth peakons to the system are both orbitally stable.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135198628","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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