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Equivariant localization in Batalin-Vilkovisky formalism Batalin-Vilkovisky形式主义中的等变局部化
IF 0.6 4区 数学
Differential Geometry and its Applications Pub Date : 2025-09-01 Epub Date: 2025-07-09 DOI: 10.1016/j.difgeo.2025.102265
Alberto S. Cattaneo, Shuhan Jiang
{"title":"Equivariant localization in Batalin-Vilkovisky formalism","authors":"Alberto S. Cattaneo,&nbsp;Shuhan Jiang","doi":"10.1016/j.difgeo.2025.102265","DOIUrl":"10.1016/j.difgeo.2025.102265","url":null,"abstract":"<div><div>We derive equivariant localization formulas of Atiyah–Bott and cohomological field theory types in the Batalin-Vilkovisky formalism and discuss their applications in Poisson geometry and quantum field theory.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"100 ","pages":"Article 102265"},"PeriodicalIF":0.6,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144579540","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 Hamilton-Souplet-Zhang type gradient estimate for a class of parabolic equations on Finsler manifolds 一类抛物型方程在Finsler流形上的Hamilton-Souplet-Zhang型梯度估计
IF 0.6 4区 数学
Differential Geometry and its Applications Pub Date : 2025-09-01 Epub Date: 2025-06-09 DOI: 10.1016/j.difgeo.2025.102264
Zisu Zhao
{"title":"A Hamilton-Souplet-Zhang type gradient estimate for a class of parabolic equations on Finsler manifolds","authors":"Zisu Zhao","doi":"10.1016/j.difgeo.2025.102264","DOIUrl":"10.1016/j.difgeo.2025.102264","url":null,"abstract":"<div><div>Employing a new Laplacian comparison theorem, we have derived a Souplet-Zhang type gradient estimate for a specific nonlinear parabolic equation (Finslerian logarithmic Schrödinger equation) on a non-compact forward complete Finsler manifold with some curvatures bounded from below. All the coefficients in our equations vary with time on the manifold. As applications, we obtain a local Harnack inequality and a Liouville-type theorem.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"100 ","pages":"Article 102264"},"PeriodicalIF":0.6,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144240986","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Rigidity of closed minimal hypersurfaces in S5 S5中闭极小超曲面的刚性
IF 0.6 4区 数学
Differential Geometry and its Applications Pub Date : 2025-09-01 Epub Date: 2025-05-09 DOI: 10.1016/j.difgeo.2025.102252
Pengpeng Cheng, Tongzhu Li
{"title":"Rigidity of closed minimal hypersurfaces in S5","authors":"Pengpeng Cheng,&nbsp;Tongzhu Li","doi":"10.1016/j.difgeo.2025.102252","DOIUrl":"10.1016/j.difgeo.2025.102252","url":null,"abstract":"<div><div>Let <span><math><msup><mrow><mi>M</mi></mrow><mrow><mn>4</mn></mrow></msup><mo>→</mo><msup><mrow><mi>S</mi></mrow><mrow><mn>5</mn></mrow></msup></math></span> be a closed immersed minimal hypersurface with constant squared length of the second fundamental form <em>S</em> in a 5-dimensional sphere <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>5</mn></mrow></msup></math></span>. In this paper, we prove that if the 3-mean curvature <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>3</mn></mrow></msub></math></span> and the number <em>g</em> of the distinct principal curvatures are constant, then <span><math><msup><mrow><mi>M</mi></mrow><mrow><mn>4</mn></mrow></msup></math></span> is an isoparametric hypersurface, and the value of <em>S</em> can only be <span><math><mn>0</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>12</mn></math></span>. This result supports Chern Conjecture.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"100 ","pages":"Article 102252"},"PeriodicalIF":0.6,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143922663","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Time in classical and quantum mechanics 经典和量子力学中的时间
IF 0.6 4区 数学
Differential Geometry and its Applications Pub Date : 2025-09-01 Epub Date: 2025-05-14 DOI: 10.1016/j.difgeo.2025.102253
J. Muñoz-Díaz, R.J. Alonso-Blanco
{"title":"Time in classical and quantum mechanics","authors":"J. Muñoz-Díaz,&nbsp;R.J. Alonso-Blanco","doi":"10.1016/j.difgeo.2025.102253","DOIUrl":"10.1016/j.difgeo.2025.102253","url":null,"abstract":"<div><div>In this article we study the nature of time in Mechanics. The fundamental principle, according to which a mechanical system evolves governed by a second order differential equation, implies the existence of an <em>absolute time-duration</em> in the sense of Newton. There is a second notion of time for conservative systems which makes the Hamiltonian action evolves at a constant rate. In Quantum Mechanics the absolute time loses its sense as it does the notion of trajectory. Then, we propose two different ways to reach the time dependent Schrödinger equation. One way consists of considering a “time constraint” on a free system. The other way is based on the point of view of Hertz, by considering the system as a projection of a free system. In the later manner, the “time” appearing in the Schrödinger equation is a linear combination of the time-duration with the “time” quotient of the action by the energy on each solution of the Hamilton-Jacobi equation. Both of them are based on a rule of quantization that we explain in Section 4.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"100 ","pages":"Article 102253"},"PeriodicalIF":0.6,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143941897","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Multisymplectic observable reduction using constraint triples 约束三元组的多辛可观察约简
IF 0.6 4区 数学
Differential Geometry and its Applications Pub Date : 2025-09-01 Epub Date: 2025-07-16 DOI: 10.1016/j.difgeo.2025.102272
Antonio Michele Miti , Leonid Ryvkin
{"title":"Multisymplectic observable reduction using constraint triples","authors":"Antonio Michele Miti ,&nbsp;Leonid Ryvkin","doi":"10.1016/j.difgeo.2025.102272","DOIUrl":"10.1016/j.difgeo.2025.102272","url":null,"abstract":"<div><div>The purpose of this paper is to present a fully algebraic formalism for the construction and reduction of <span><math><msub><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span>-algebras of observables inspired by multisymplectic geometry, using Gerstenhaber algebras, BV-modules, and the constraint triple formalism. In the “geometric case”, we reconstruct and conceptually explain the recent results of <span><span>[7]</span></span>.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"100 ","pages":"Article 102272"},"PeriodicalIF":0.6,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144634476","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Orlicz harmonic version of dual mixed volumes 奥尔利茨调和版的双混合卷
IF 0.6 4区 数学
Differential Geometry and its Applications Pub Date : 2025-09-01 Epub Date: 2025-07-02 DOI: 10.1016/j.difgeo.2025.102268
Chang-Jian Zhao
{"title":"Orlicz harmonic version of dual mixed volumes","authors":"Chang-Jian Zhao","doi":"10.1016/j.difgeo.2025.102268","DOIUrl":"10.1016/j.difgeo.2025.102268","url":null,"abstract":"<div><div>In the paper, our main aim is to generalize the dual mixed harmonic quermassintegrals to Orlicz space. Under the framework of Orlicz dual Brunn-Minkowski theory, we introduce a new affine geometric quantity by calculating Orlicz first order variation of the dual mixed harmonic quermassintegrals, and call it the Orlicz dual mixed harmonic quermassintegrals. The fundamental notions and conclusions of the dual mixed harmonic quermassintegrals and the Minkowski and Brunn-Minkowski inequalities for the dual harmonic quermassintegrals are extended to an Orlicz setting, and the related concepts and inequalities of Orlicz dual mixed volumes are also included in our conclusions.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"100 ","pages":"Article 102268"},"PeriodicalIF":0.6,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144534227","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Higher-power harmonic maps, instantons and Yang-Mills theory 高功率谐波映射，瞬子和杨-米尔斯理论
IF 0.6 4区 数学
Differential Geometry and its Applications Pub Date : 2025-06-01 Epub Date: 2025-03-09 DOI: 10.1016/j.difgeo.2025.102240
Elias Knack, Henrik Naujoks
{"title":"Higher-power harmonic maps, instantons and Yang-Mills theory","authors":"Elias Knack,&nbsp;Henrik Naujoks","doi":"10.1016/j.difgeo.2025.102240","DOIUrl":"10.1016/j.difgeo.2025.102240","url":null,"abstract":"<div><div>Let <span><math><mo>(</mo><mi>M</mi><mo>,</mo><mi>g</mi><mo>)</mo></math></span> and <span><math><mo>(</mo><mi>N</mi><mo>,</mo><mi>h</mi><mo>)</mo></math></span> be two pseudo-Riemannian manifolds. We study field theoretic properties of higher-power harmonic maps (also called <em>r</em>-harmonic maps) <span><math><mi>φ</mi><mo>:</mo><mi>M</mi><mo>→</mo><mi>N</mi></math></span>, which are a natural generalization of standard harmonic maps first introduced by C. Wood. In particular, we discuss the coupled system of higher-power harmonic maps and the Einstein-Hilbert action and prove a sufficient condition for a map to be <em>r</em>-harmonic, which is highly motivated by classical field equations like the harmonic map equation or the Yang-Mills equation. Furthermore, we derive an instanton theory for <em>r</em>-harmonic maps on 2<em>r</em>-dimensional base manifolds and investigate conformal properties of general higher-power harmonic maps. Finally, since the theory of higher-power harmonic maps bears striking similarities with Yang-Mills theory, we provide a comprehensive comparison between the two theories which explains in more detail surprisingly many analogies.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"99 ","pages":"Article 102240"},"PeriodicalIF":0.6,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143580361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Regulated curves on a Banach manifold and singularities of endpoint map. I. Banach manifold structure Banach流形上的调节曲线及端点映射的奇异性。1 .巴拿赫流形结构
IF 0.6 4区 数学
Differential Geometry and its Applications Pub Date : 2025-06-01 Epub Date: 2025-03-27 DOI: 10.1016/j.difgeo.2025.102245
Tomasz Goliński , Fernand Pelletier
{"title":"Regulated curves on a Banach manifold and singularities of endpoint map. I. Banach manifold structure","authors":"Tomasz Goliński ,&nbsp;Fernand Pelletier","doi":"10.1016/j.difgeo.2025.102245","DOIUrl":"10.1016/j.difgeo.2025.102245","url":null,"abstract":"<div><div>We consider regulated curves in a Banach bundle whose projection on the basis is continuous with regulated derivative. We build a Banach manifold structure on the set of such curves. This result was previously obtained for the case of strong Riemannian Banach manifold and absolutely continuous curves in <span><span>[16]</span></span>. The essential argument used was the existence of a “local addition” on such a manifold. Our proof is true for any Banach manifold. In the second part of the paper the problems of controllability will be discussed.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"99 ","pages":"Article 102245"},"PeriodicalIF":0.6,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143706392","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
On the integration of Manin pairs 关于Manin对的积分
IF 0.6 4区 数学
Differential Geometry and its Applications Pub Date : 2025-06-01 Epub Date: 2025-04-04 DOI: 10.1016/j.difgeo.2025.102246
David Li-Bland, Eckhard Meinrenken
{"title":"On the integration of Manin pairs","authors":"David Li-Bland,&nbsp;Eckhard Meinrenken","doi":"10.1016/j.difgeo.2025.102246","DOIUrl":"10.1016/j.difgeo.2025.102246","url":null,"abstract":"<div><div>It is a remarkable fact that the integrability of a Poisson manifold to a symplectic groupoid depends only on the integrability of its cotangent Lie algebroid <em>A</em>: The source-simply connected Lie groupoid <span><math><mi>G</mi><mo>⇉</mo><mi>M</mi></math></span> integrating <em>A</em> automatically acquires a multiplicative symplectic 2-form. More generally, a similar result holds for the integration of Lie bialgebroids to Poisson groupoids, as well as in the ‘quasi’ settings of Dirac structures and quasi-Lie bialgebroids. In this article, we will place these results into a general context of Manin pairs <span><math><mo>(</mo><mi>E</mi><mo>,</mo><mi>A</mi><mo>)</mo></math></span>, thereby obtaining a simple geometric approach to these integration results. We also clarify the case where the groupoid <em>G</em> integrating <em>A</em> is not source-simply connected. Furthermore, we obtain a description of Hamiltonian spaces for Poisson groupoids and quasi-symplectic groupoids within this formalism.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"99 ","pages":"Article 102246"},"PeriodicalIF":0.6,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143768267","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Ramification and unicity theorems for Gauss maps of complete space-like stationary surfaces in four-dimensional Lorentz-Minkowski space 四维洛伦兹-闵可夫斯基空间中完全类空固定曲面高斯映射的分支和唯一性定理
IF 0.6 4区 数学
Differential Geometry and its Applications Pub Date : 2025-06-01 Epub Date: 2025-02-27 DOI: 10.1016/j.difgeo.2025.102238
Li Ou
{"title":"Ramification and unicity theorems for Gauss maps of complete space-like stationary surfaces in four-dimensional Lorentz-Minkowski space","authors":"Li Ou","doi":"10.1016/j.difgeo.2025.102238","DOIUrl":"10.1016/j.difgeo.2025.102238","url":null,"abstract":"<div><div>In this paper, we investigate value distribution properties for Gauss maps of space-like stationary surfaces in four-dimensional Lorentz-Minkowski space <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn><mo>,</mo><mn>1</mn></mrow></msup></math></span>, focusing on aspects such as the total weight of totally ramified values and unicity properties. We obtain not only general conclusions analogous to those in four-dimensional Euclidean space, but also results for space-like stationary surfaces with rational graphical Gauss image, which is an extension of degenerate space-like stationary surfaces.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"99 ","pages":"Article 102238"},"PeriodicalIF":0.6,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143510165","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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