Acta Mathematica Sinica-English Series最新文献

{"title":"Spectral Invariance in Dense Subalgebras of Uniform Roe Algebras","authors":"Siqi Jiang,&nbsp;Xianjin Wang","doi":"10.1007/s10114-026-5223-5","DOIUrl":"10.1007/s10114-026-5223-5","url":null,"abstract":"<div><p>The article [Chen, X., Wang, X., Wang, Q.: Truncation approximations and spectral invariant subalgebras in uniform Roe algebras of discrete groups. <i>J. Fourier Anal. Appl.</i>, <b>21</b>, 555–574 (2015)] investigated spectral subalgebras of the uniform Roe algebra, although their Theorem 4.7 on spectral invariance contains a gap. To address this gap, we construct a class of Fréchet subalgebras using polynomial growth weights and prove that these algebras are not only spectrally invariant but also dense in the uniform Roe algebra for groups of polynomial growth–thereby completing and extending the earlier results.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 4","pages":"1135 - 1148"},"PeriodicalIF":0.9,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147827029","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}

{"title":"A Duality Principle for Holomorphic Isometric Embeddings of the Complex Unit Ball into Bounded Symmetric Domains","authors":"Ngaiming Mok","doi":"10.1007/s10114-026-5014-z","DOIUrl":"10.1007/s10114-026-5014-z","url":null,"abstract":"&lt;div&gt;&lt;p&gt;The sources of our investigation are the author’s constructions of nonstandard &lt;i&gt;bona fide&lt;/i&gt; holomorphic isometric embeddings called &lt;i&gt;p&lt;/i&gt;-th root maps of the Poincaré upper half-plane into Cartesian products of identical copies of itself, and those of complex unit balls &lt;span&gt;(mathbb{B}^{p(Omega)+1})&lt;/span&gt; of maximal admissible dimension into irreducible bounded symmetric domains Ω of rank ≥ 2 whose images are full cones &lt;i&gt;V&lt;/i&gt;&lt;sub&gt;&lt;i&gt;b&lt;/i&gt;&lt;/sub&gt; of minimal disks, &lt;i&gt;b&lt;/i&gt; ∈ Reg(∂Ω). In this article we give a proof of a duality principle for holomorphic isometric embeddings of the complex unit ball &lt;span&gt;(mathbb{B}^{m})&lt;/span&gt;, &lt;i&gt;m&lt;/i&gt; ≥ 1 into an irreducible bounded symmetric domain Ω. Identify Ω by means of the Borel embedding as an open subset of its dual Hermitian symmetric space &lt;span&gt;(widehat{Omega})&lt;/span&gt; of the compact type. Let &lt;span&gt;(f:(mathbb{B}^{m},g_{m})rightarrow(Omega, h))&lt;/span&gt; be a holomorphic isometry, where &lt;i&gt;g&lt;/i&gt;&lt;sub&gt;&lt;i&gt;m&lt;/i&gt;&lt;/sub&gt; resp. &lt;i&gt;h&lt;/i&gt; denotes the canonical Kähler–Einstein metric on &lt;span&gt;(mathbb{B}^{m})&lt;/span&gt; resp. Ω normalized so that minimal disks are of constant Gaussian curvature −2, and assume &lt;span&gt;(0in f(mathbb{B}^{m})=:Z)&lt;/span&gt;. Choosing a dual pair (&lt;i&gt;G&lt;/i&gt;&lt;sub&gt;0&lt;/sub&gt;, &lt;i&gt;G&lt;/i&gt;&lt;sub&gt;&lt;i&gt;c&lt;/i&gt;&lt;/sub&gt;) of noncompact resp. compact real forms of the connected simple complex Lie group &lt;i&gt;G&lt;/i&gt; which is the identity component of &lt;span&gt;(text{Aut}(widehat{Omega}))&lt;/span&gt; so that &lt;i&gt;G&lt;/i&gt;&lt;sub&gt;0&lt;/sub&gt; ∩ &lt;i&gt;G&lt;/i&gt;&lt;sub&gt;&lt;i&gt;c&lt;/i&gt;&lt;/sub&gt; = &lt;i&gt;K&lt;/i&gt; is the isotropy subgroup of &lt;i&gt;G&lt;/i&gt;&lt;sub&gt;0&lt;/sub&gt; at 0 ∈ Ω, and denoting by &lt;i&gt;g&lt;/i&gt; the &lt;i&gt;G&lt;/i&gt;&lt;sub&gt;&lt;i&gt;c&lt;/i&gt;&lt;/sub&gt;-invariant Kähler–Einstein metric normalized so that minimal rational curves are of constant Gaussian curvature +2, the curvature tensors of (Ω, &lt;i&gt;h&lt;/i&gt;) and &lt;span&gt;((widehat{Omega},g))&lt;/span&gt; at &lt;span&gt;(0 in Omega subsetwidehat{Omega})&lt;/span&gt; are opposite to each other. Basing on the latter fact and comparing the two holomorphic isometric embeddings &lt;span&gt;(f:mathbb{B}^{m}rightarrowOmega)&lt;/span&gt; resp. &lt;span&gt;(nu:widehat{Omega}rightarrowmathbb{P}^{N})&lt;/span&gt;, where the latter denotes the minimal projective embedding of &lt;span&gt;(widehat{Omega})&lt;/span&gt;, we obtain an identity on the lengths of the two second fundamental forms &lt;i&gt;σ&lt;/i&gt; resp. &lt;i&gt;τ&lt;/i&gt; applied to a pair of holomorphic tangent vectors &lt;i&gt;ξ, η&lt;/i&gt; ∈ &lt;i&gt;T&lt;/i&gt;&lt;sub&gt;0&lt;/sub&gt;(Ω), and we call this the &lt;i&gt;duality principle&lt;/i&gt; for holomorphic isometric embeddings of the complex unit ball into irreducible bounded symmetric domains. This duality principle yields constraints on isomorphism types of holomorphic tangent spaces of holomorphic isometric images &lt;i&gt;Z&lt;/i&gt; ⊂ Ω of the complex unit ball, and it serves as the basis of uniqueness results on nonstandard holomorphic isometric embeddings &lt;span&gt;(f:mathbb{B}^{p(Omega)+1}rightarrow{Omega})&lt;/span&gt; of complex unit balls of maximal admissible dimension into Ω. By varying the base points we also amplify the duality principle to an identity on second fund","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 on","pages":"1403 - 1430"},"PeriodicalIF":0.9,"publicationDate":"2026-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148173018","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}

{"title":"Number Rigid Determinantal Point Processes Induced by Generalized Cantor Sets","authors":"Zhaofeng Lin,&nbsp;Yanqi Qiu,&nbsp;Kai Wang","doi":"10.1007/s10114-026-4384-6","DOIUrl":"10.1007/s10114-026-4384-6","url":null,"abstract":"<div><p>We consider the Ghosh–Peres number rigidity of translation-invariant determinantal point processes on the real line ℝ, whose correlation kernels are induced by the Fourier transform of the indicators of generalized Cantor sets in the unit interval. Our main results show that for any given <i>θ</i> ∈ (0, 1), there exists a generalized Cantor set with Lebesgue measure <i>θ</i>, such that the corresponding determinantal point process is Ghosh–Peres number rigid.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 on","pages":"1595 - 1608"},"PeriodicalIF":0.9,"publicationDate":"2026-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148261987","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}

{"title":"Convergence of the Kähler–Ricci Flow on Minimal Models of General Type","authors":"Wangjian Jian,&nbsp;Jian Song","doi":"10.1007/s10114-026-4052-x","DOIUrl":"10.1007/s10114-026-4052-x","url":null,"abstract":"<div><p>The Kähler–Ricci flow always admits a long time solution on a smooth minimal model <i>X</i> of general type. We show that the normalized solution converges in Gromov–Hausdorff sense to the unique compact Kähler–Einstein metric space homeomorphic to the algebraic canonical model <i>X</i>_can of <i>X</i>.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 on","pages":"1373 - 1386"},"PeriodicalIF":0.9,"publicationDate":"2026-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148173017","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}

{"title":"Towards the Symplectic Graber–Harris–Starr Theorems","authors":"Zhiyu Tian","doi":"10.1007/s10114-026-5298-z","DOIUrl":"10.1007/s10114-026-5298-z","url":null,"abstract":"<div><p>A theorem of Graber, Harris, and Starr states that a rationally connected fibration over a curve has a section. We study an analogous question in symplectic geometry. Namely, given a rationally connected fibration over a curve, can one find a section which gives a non-zero Gromov–Witten invariant? We observe that for any fibration, the existence of a section which gives a non-zero Gromov–Witten invariant only depends on the generic fiber, i.e., a variety defined over the function field of a curve. Some examples of rationally connected fibrations with this property are given, including all rational surface fibrations. We also prove some results, which says that in certain cases we can “lift” Gromov–Witten invariants of the base to the total space of a rationally connected fibration.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 3","pages":"791 - 805"},"PeriodicalIF":0.9,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147752465","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}

{"title":"K-Theory Methods in Solid State Physics","authors":"Armen Sergeev","doi":"10.1007/s10114-026-4634-7","DOIUrl":"10.1007/s10114-026-4634-7","url":null,"abstract":"<div><p>This paper is a review of <i>K</i>-theory methods in solid state physics. Our goal is to demonstrate that <i>K</i>-theory is a natural language for the mathematical description of solid bodies. Our main tool is the <i>K</i>-theory of <i>C</i>*-algebras. We follow Kitaev’s idea that the symmetry algebras of solid bodies belong to the class of Clifford algebras which reduces the quantization problem for solid states to the representation theory of Clifford algebras.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 3","pages":"583 - 602"},"PeriodicalIF":0.9,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147752467","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}

{"title":"The Critical Power of Short Pulse Initial Data on the Global Existence or Blowup of Smooth Solutions to 3-D Semilinear Klein–Gordon Equations","authors":"Jindou Shen,&nbsp;Huicheng Yin","doi":"10.1007/s10114-026-4633-8","DOIUrl":"10.1007/s10114-026-4633-8","url":null,"abstract":"<div><p>It is well-known that there are global small data smooth solutions for the 3-D semilinear Klein–Gordon equations □<i>u</i> + <i>u</i> = <i>F</i>(<i>u, ∂u</i>) with cubic nonlinearities. However, for the short pulse initial data <span>((u,partial_{t}u)(0,x)=(delta^{nu+1}u_{0}({xover delta}),delta^{nu}u_{1}({xover delta})))</span> with <i>ν</i> ∈ ℝ and (<i>u</i>₀, <i>u</i>₁) ∈ <i>C</i><span>\u0000 ^∞₀\u0000 \u0000 </span>(ℝ), which are a class of large initial data, we establish that when <span>(nuleq-{1over 2})</span>, the solution <i>u</i> can blow up in finite time for some suitable choices of (<i>u</i>₀, <i>u</i>₁) and cubic nonlinearity <i>F</i>(<i>u</i>, <i>∂u</i>); when <span>(nu &gt;-{1over 2})</span>, the smooth solution <i>u</i> exists globally. Therefore, <span>(nu=-{1over 2})</span> is just the critical power corresponding to the global existence or blowup of smooth short pulse solutions for the cubic semilinear Klein–Gordon equations.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 3","pages":"568 - 582"},"PeriodicalIF":0.9,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147752466","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}

{"title":"Formal Manifolds: Local Structure of Morphisms, and Formal Submanifolds","authors":"Fulin Chen,&nbsp;Binyong Sun,&nbsp;Chuyun Wang","doi":"10.1007/s10114-026-5046-4","DOIUrl":"10.1007/s10114-026-5046-4","url":null,"abstract":"<div><p>This is a paper in a series that studies smooth relative Lie algebra homologies and cohomologies based on the theory of formal manifolds and formal Lie groups. In three previous papers, we introduce the notion of formal manifolds and study their basic theory, focusing on function spaces and Poincaré’s lemma. In this paper, we further explore the foundational framework of formal manifolds, including the local structure of constant rank morphisms (such as inverse function theorem and constant rank theorems) as well as the theory of formal submanifolds.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 3","pages":"603 - 647"},"PeriodicalIF":0.9,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147752461","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}

{"title":"Nilpotent Structures in Dynamical Systems","authors":"Wen Huang,&nbsp;Jiahao Qiu,&nbsp;Song Shao,&nbsp;Xiangdong Ye","doi":"10.1007/s10114-026-5336-x","DOIUrl":"10.1007/s10114-026-5336-x","url":null,"abstract":"<div><p>The investigation of nilpotent structures aims to uncover the underlying nilpotent information in general dynamical systems, as well as the dynamical behaviors of the systems with respect to the nilpotent structures. These structures play crucial roles in ergodic theory and topological dynamics, and their applications across several fields of mathematics, including combinatorial number theory.</p><p>In this paper we will review the results related to the nilpotent structures, with a particular emphasis on topological nilpotent structures of ℤ-actions. Furthermore, we present applications and state open questions for future research.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 3","pages":"755 - 790"},"PeriodicalIF":0.9,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147752473","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}

{"title":"H-invariant and Its Applications","authors":"Gang Tian,&nbsp;Xiaohua Zhu","doi":"10.1007/s10114-026-5435-8","DOIUrl":"10.1007/s10114-026-5435-8","url":null,"abstract":"<div><p>The <i>H</i>-invariant was introduced to compute Perelmans entropy for Kähler–Ricci flow in a paper of Tian–Zhang–Zhang–Zhu more than ten years ago. It turns out that the <i>H</i>-invariant is equal to an earlier invariant by Tian–Zhu in their study on Kähler–Ricci solitons. In this largely expository paper, we will discuss definition of the <i>H</i>-invariant, its relation to Tian–Zhu’s generalization of the Futaki invariants as well as some of its applications. We will also include some new observations and generalizations of results in existing literature. Several examples will be also provided.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 3","pages":"881 - 912"},"PeriodicalIF":0.9,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147752475","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}