Communications in Contemporary Mathematics最新文献

{"title":"Maximal directional derivatives in Laakso space","authors":"Marco Capolli, Andrea Pinamonti, Gareth Speight","doi":"10.1142/s0219199724500172","DOIUrl":"https://doi.org/10.1142/s0219199724500172","url":null,"abstract":"<p>We investigate the connection between maximal directional derivatives and differentiability for Lipschitz functions defined on Laakso space. We show that maximality of a directional derivative for a Lipschitz function implies differentiability only for a <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>σ</mi></math></span><span></span>-porous set of points. On the other hand, the distance to a fixed point is differentiable everywhere except for a <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>σ</mi></math></span><span></span>-porous set of points. This behavior is completely different to the previously studied settings of Euclidean spaces, Carnot groups and Banach spaces. Hence, the techniques used in these spaces do not generalize to metric measure spaces.</p>","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":"37 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141150969","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Smooth modules over the N = 1 Bondi–Metzner–Sachs superalgebra","authors":"Dong Liu, Yufeng Pei, Limeng Xia, Kaiming Zhao","doi":"10.1142/s0219199724500214","DOIUrl":"https://doi.org/10.1142/s0219199724500214","url":null,"abstract":"<p>In this paper, we present a determinant formula for a contravariant form on Verma modules over the <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mstyle mathvariant=\"italic\"><mi>N</mi></mstyle><mo>=</mo><mn>1</mn></math></span><span></span> Bondi–Metzner–Sachs (BMS) superalgebra. This formula establishes a necessary and sufficient condition for the irreducibility of the Verma modules. We then introduce and characterize a class of simple smooth modules that generalize both Verma and Whittaker modules over the <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mstyle mathvariant=\"italic\"><mi>N</mi></mstyle><mo>=</mo><mn>1</mn></math></span><span></span> BMS superalgebra. We also utilize the Heisenberg–Clifford vertex superalgebra to construct a free field realization for the <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mstyle mathvariant=\"italic\"><mi>N</mi></mstyle><mo>=</mo><mn>1</mn></math></span><span></span> BMS superalgebra. This free field realization allows us to obtain a family of natural smooth modules over the <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><mstyle mathvariant=\"italic\"><mi>N</mi></mstyle><mo>=</mo><mn>1</mn></math></span><span></span> BMS superalgebra, which includes Fock modules and certain Whittaker modules.</p>","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":"89 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141150970","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Pseudoconvex submanifolds in Kähler 4-manifolds","authors":"Brian Weber","doi":"10.1142/s0219199724500147","DOIUrl":"https://doi.org/10.1142/s0219199724500147","url":null,"abstract":"<p>This paper shows how a Levi-flat or pseudoconvex submanifold in a Kähler 4-manifold restricts the ambient manifold’s topology and its geometry at infinity.</p>","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":"36 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140925663","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A characterization of the subspace of radially symmetric functions in Sobolev spaces","authors":"Matthias Ostermann","doi":"10.1142/s0219199724500184","DOIUrl":"https://doi.org/10.1142/s0219199724500184","url":null,"abstract":"<p>In this paper, we show that any Sobolev norm of nonnegative integer order of radially symmetric functions is equivalent to a weighted Sobolev norm of their radial profile. This establishes in terms of weighted Sobolev spaces on an interval a complete characterization of radial Sobolev spaces, which was open until now. As an application, we give a description of Sobolev norms of corotational maps.</p>","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":"6 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140925773","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A moment map for the variety of Jordan algebras","authors":"Claudio Gorodski, Iryna Kashuba, María Eugenia Martin","doi":"10.1142/s0219199724500159","DOIUrl":"https://doi.org/10.1142/s0219199724500159","url":null,"abstract":"<p>We study the variety of complex <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>n</mi></math></span><span></span>-dimensional Jordan algebras using techniques from Geometric Invariant Theory. More specifically, we use the Kirwan–Ness theorem to construct a Morse-type stratification of the variety of Jordan algebras into finitely many invariant locally closed subsets, with respect to the energy functional associated to the canonical moment map. In particular we obtain a new, cohomology-free proof of the well-known rigidity of semisimple Jordan algebras in the context of the variety of Jordan algebras.</p>","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":"47 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140942339","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Pointwise convergence of the heat and subordinates of the heat semigroups associated with the Laplace operator on homogeneous trees and two weighted Lp maximal inequalities","authors":"I. Alvarez-Romero, B. Barrios, J. J. Betancor","doi":"10.1142/s021919972450010x","DOIUrl":"https://doi.org/10.1142/s021919972450010x","url":null,"abstract":"&lt;p&gt;In this paper, we consider the heat semigroup &lt;span&gt;&lt;math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo stretchy=\"false\"&gt;{&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;W&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo stretchy=\"false\"&gt;}&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt; defined by the combinatorial Laplacian and two subordinated families of &lt;span&gt;&lt;math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo stretchy=\"false\"&gt;{&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;W&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo stretchy=\"false\"&gt;}&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt; on homogeneous trees &lt;span&gt;&lt;math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt;. We characterize the weights &lt;span&gt;&lt;math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt; on &lt;span&gt;&lt;math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt; for which the pointwise convergence to initial data of the above families holds for every &lt;span&gt;&lt;math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo stretchy=\"false\"&gt;(&lt;/mo&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo stretchy=\"false\"&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt; with &lt;span&gt;&lt;math altimg=\"eq-00008.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;∞&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt;, where &lt;span&gt;&lt;math altimg=\"eq-00009.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt; represents the counting measure in &lt;span&gt;&lt;math altimg=\"eq-00010.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt;. We prove that this convergence property in &lt;span&gt;&lt;math altimg=\"eq-00011.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt; is equivalent to the fact that the maximal operator on &lt;span&gt;&lt;math altimg=\"eq-00012.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mo stretchy=\"false\"&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;mo stretchy=\"false\"&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt;, for some &lt;span&gt;&lt;math altimg=\"eq-00013.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt;, defined by the semigroup is bounded from &lt;span&gt;&lt;math altimg=\"eq-00014.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo stretchy=\"false\"&gt;(&lt;/mo&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo stretchy=\"false\"&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt; into &lt;span&gt;&lt;math altimg=\"eq-00015.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo stretchy=\"false\"&gt;(&lt;/mo&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo stretchy=\"false\"&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt; for some weight &lt;span&gt;&lt;math altimg=\"eq-00016.g","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":"21 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140626157","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Double Yangian and reflection algebras of the Lie superalgebra 𝔤𝔩m|n","authors":"Lucia Bagnoli, Slaven Kožić","doi":"10.1142/s021919972450007x","DOIUrl":"https://doi.org/10.1142/s021919972450007x","url":null,"abstract":"<p>We study the double Yangian associated with the Lie superalgebra <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>𝔤</mi><mi>𝔩</mi></mrow><mrow><mi>m</mi><mo>|</mo><mi>n</mi></mrow></msub></math></span><span></span>. Our main focus is on establishing the Poincaré–Birkhoff–Witt Theorem for the double Yangian and constructing its central elements in the form of coefficients of the quantum contraction. Next, as an application, we introduce reflection algebras, certain left coideal subalgebras of the level 0 double Yangian, and find their presentations by generators and relations.</p>","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":"26 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140614802","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The complex hyperbolic form as a Weil–Petersson form","authors":"Xiangsheng Wang","doi":"10.1142/s0219199724500068","DOIUrl":"https://doi.org/10.1142/s0219199724500068","url":null,"abstract":"<p>For the moduli space of the punctured spheres, we find a new equality between two symplectic forms defined on it. Namely, by treating the elements of this moduli space as the singular Euclidean metrics on a sphere, we give an interpretation of the complex hyperbolic form, i.e. the Kähler form of the complex hyperbolic structure on the moduli space, as a kind of Weil–Petersson form.</p>","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":"24 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140614843","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Subsonic flows with a contact discontinuity in a finitely long axisymmetric cylinder","authors":"Shangkun Weng, Zihao Zhang","doi":"10.1142/s0219199724500081","DOIUrl":"https://doi.org/10.1142/s0219199724500081","url":null,"abstract":"<p>This paper concerns the structural stability of subsonic flows with a contact discontinuity in a finitely long axisymmetric cylinder. We establish the existence and uniqueness of axisymmetric subsonic flows with a contact discontinuity by prescribing the horizontal mass flux distribution, the swirl velocity, the entropy and the Bernoulli’s quantity at the entrance and the radial velocity at the exit. It can be formulated as a free boundary problem with the contact discontinuity to be determined simultaneously with the flows. Compared with the two-dimensional case, a new difficulty arises due to the singularity near the axis. An invertible modified Lagrangian transformation is introduced to overcome this difficulty and straighten the contact discontinuity. The key elements in our analysis are to utilize the deformation-curl decomposition introduced in [S. Weng and Z. Xin, A deformation-curl decomposition for three dimensional steady Euler equations, <i>Sci. Sin. Math.</i><b>49</b> (2019) 307–320 (in Chinese): doi:10.1360/N012018-00125] to effectively decouple the hyperbolic and elliptic modes in the steady axisymmetric Euler system and to use the implicit function theorem to locate the contact discontinuity.</p>","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":"3 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140573476","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Sharp spectral gap estimates for higher-order operators on Cartan–Hadamard manifolds","authors":"Csaba Farkas, Sándor Kajántó, Alexandru Kristály","doi":"10.1142/s0219199724500135","DOIUrl":"https://doi.org/10.1142/s0219199724500135","url":null,"abstract":"<p>The goal of this paper is to provide sharp spectral gap estimates for problems involving higher-order operators (including both the clamped and buckling plate problems) on Cartan–Hadamard manifolds. The proofs are symmetrization-free — thus no sharp isoperimetric inequality is needed — based on two general, yet elementary functional inequalities. The spectral gap estimate for clamped plates solves a sharp asymptotic problem from [Q.-M. Cheng and H. Yang, Universal inequalities for eigenvalues of a clamped plate problem on a hyperbolic space, <i>Proc. Amer. Math. Soc.</i><b>139</b>(2) (2011) 461–471] concerning the behavior of higher-order eigenvalues on hyperbolic spaces, and answers a question raised in [A. Kristály, Fundamental tones of clamped plates in nonpositively curved spaces, <i>Adv. Math.</i><b>367</b>(39) (2020) 107113] on the validity of such sharp estimates in high-dimensional Cartan–Hadamard manifolds. As a byproduct of the general functional inequalities, various Rellich inequalities are established in the same geometric setting.</p>","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":"24 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140573507","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}