arXiv - MATH - Differential Geometry最新文献_第6页

On minimal hypersurfaces in Euclidean spaces and Riemannian manifolds 论欧几里得空间和黎曼流形中的最小超曲面

arXiv - MATH - Differential Geometry Pub Date : 2024-09-06 DOI: arxiv-2409.04426

Josef Mikes, Sergey Stepanov, Irina Tsyganok

引用次数: 0

The geometric Cauchy problem for constant-rank submanifolds 恒等阶子漫游的几何考奇问题

arXiv - MATH - Differential Geometry Pub Date : 2024-09-06 DOI: arxiv-2409.04358

Matteo Raffaelli

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Compact holonomy $mathrm{G}_2$ manifolds need not be formal 紧凑整体性 $mathrm{G}_2$ 流形不必是形式的

arXiv - MATH - Differential Geometry Pub Date : 2024-09-06 DOI: arxiv-2409.04362

Lucía Martín-Merchán

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The Dirichlet problem for a class of curvature equations in Minkowski space 闵科夫斯基空间一类曲率方程的迪里夏特问题

arXiv - MATH - Differential Geometry Pub Date : 2024-09-05 DOI: arxiv-2409.03308

Mengru Guo, Heming Jiao

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Monotonicity Formulas for Capillary Surfaces 毛细管表面的单调性公式

arXiv - MATH - Differential Geometry Pub Date : 2024-09-05 DOI: arxiv-2409.03314

Guofang Wang, Chao Xia, Xuwen Zhang

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On the stability of free boundary minimal submanifolds in conformal domains 论保形域中自由边界最小子曼形体的稳定性

arXiv - MATH - Differential Geometry Pub Date : 2024-09-05 DOI: arxiv-2409.03943

Alcides de Carvalho, Roney Santos, Federico Trinca

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Critical domains for certain Dirichlet integrals in weighted manifolds 加权流形中某些德里赫特积分的临界域

arXiv - MATH - Differential Geometry Pub Date : 2024-09-05 DOI: arxiv-2409.03554

Levi Lopes de Lima

{"title":"Critical domains for certain Dirichlet integrals in weighted manifolds","authors":"Levi Lopes de Lima","doi":"arxiv-2409.03554","DOIUrl":"https://doi.org/arxiv-2409.03554","url":null,"abstract":"We start by revisiting the derivation of the variational formulae for the\u0000functional assigning to a bounded regular domain in a Riemannian manifold its\u0000first Dirichlet eigenvalue and extend it to (not necessarily bounded) domains\u0000in certain weighted manifolds. This is further extended to other functionals\u0000defined by certain Dirichlet energy integrals, with a Morse index formula for\u0000the corresponding critical domains being established. We complement these\u0000infinitesimal results by proving a couple of global rigidity theorems for\u0000(possibly critical) domains in Gaussian half-space, including an\u0000Alexandrov-type soap bubble theorem. Although we provide direct proofs of these\u0000latter results, we find it worthwhile to point out that the main tools employed\u0000(specifically, certain Pohozhaev and Reilly identities) can be formally\u0000understood as limits (when the dimension goes to infinity) of tools previously\u0000established by Ciarolo-Vezzoni and Qiu-Xia to handle similar problems in round\u0000hemispheres, with the notion of ``convergence'' of weighted manifolds being\u0000loosely inspired by the celebrated Poincar'e's limit theorem in the theory of\u0000Gaussian random vectors.","PeriodicalId":501113,"journal":{"name":"arXiv - MATH - Differential Geometry","volume":"33 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142199037","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

OGRePy: An Object-Oriented General Relativity Package for Python OGRePy：面向对象的 Python 广义相对论软件包

arXiv - MATH - Differential Geometry Pub Date : 2024-09-05 DOI: arxiv-2409.03803

Barak Shoshany

{"title":"OGRePy: An Object-Oriented General Relativity Package for Python","authors":"Barak Shoshany","doi":"arxiv-2409.03803","DOIUrl":"https://doi.org/arxiv-2409.03803","url":null,"abstract":"We present OGRePy, the official Python port of the popular Mathematica tensor\u0000calculus package OGRe (Object-Oriented General Relativity) - a powerful, yet\u0000user-friendly, tool for advanced tensor calculations in mathematics and\u0000physics, especially suitable for general relativity. The Python port uses the\u0000same robust and performance-oriented algorithms as the original package, and\u0000retains its core design principles. However, its truly object-oriented\u0000interface, enabled by Python, is more intuitive and flexible than the original\u0000Mathematica implementation. It utilizes SymPy for symbolic computations and\u0000Jupyter as a notebook interface. OGRePy allows calculating arbitrary tensor\u0000formulas using any combination of addition, multiplication by scalar, trace,\u0000contraction, partial derivative, covariant derivative, and permutation of\u0000indices. Transformations of the tensor components between different index\u0000configurations and/or coordinate systems are performed seamlessly behind the\u0000scenes as needed, eliminating user error due to combining incompatible\u0000representations, and guaranteeing consistent results. In addition, the package\u0000provides facilities for easily calculating various curvature tensors and\u0000geodesic equations in multiple representations. This paper presents the main\u0000features of the package in great detail, including many examples of its use in\u0000the context of general relativity research.","PeriodicalId":501113,"journal":{"name":"arXiv - MATH - Differential Geometry","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142199035","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

$G_2$-instantons on the ALC members of the $mathbb{B}_7$ family $mathbb{B}_7$ 家族的 ALC 成员上的 $G_2$- nstantons

arXiv - MATH - Differential Geometry Pub Date : 2024-09-05 DOI: arxiv-2409.03886

Jakob Stein, Matt Turner

引用次数: 0

All-orders moduli for type II flux backgrounds II 型通量背景的全阶模量

arXiv - MATH - Differential Geometry Pub Date : 2024-09-05 DOI: arxiv-2409.03847

George R. Smith, David Tennyson, Daniel Waldram

{"title":"All-orders moduli for type II flux backgrounds","authors":"George R. Smith, David Tennyson, Daniel Waldram","doi":"arxiv-2409.03847","DOIUrl":"https://doi.org/arxiv-2409.03847","url":null,"abstract":"We investigate the old problem of determining the exact bulk moduli of\u0000generic $mathrm{SU}(3)$-structure flux backgrounds of type II string theory.\u0000Using techniques from generalised geometry, we show that the infinitesimal\u0000deformations are counted by a spectral sequence in which the vertical maps are\u0000either de Rham or Dolbeault differentials (depending on the type of the\u0000exceptional complex structure (ECS)) and the horizontal maps are linear maps\u0000constructed from the flux and intrinsic torsion. Our calculation is exact,\u0000covering all possible supergravity $mathrm{SU}(3)$-structure flux backgrounds\u0000including those which are not conformally Calabi--Yau, and goes beyond the\u0000usual linear approximation in three important ways: (i) we allow for finite\u0000flux; (ii) we consider perturbative higher-derivative corrections to the\u0000supergravity action; and (iii) we consider obstructions arising from\u0000higher-order deformations. Despite these extensions we find that the spectral\u0000sequence reproduces the na\"ive expectations that come from considering the\u0000effective superpotential in the small-flux limit. In particular, by writing the\u0000moduli in a form that is independent of the K\"ahler potential on the space of\u0000ECSs, and arguing the superpotential does not receive higher-derivative\u0000corrections, we show that the spectral sequence is perturbatively exact.\u0000Further, preliminary results show that a Tian--Todorov-like lemma implies that\u0000all the obstructions vanish. This has implications for the tadpole conjecture,\u0000showing that such perturbative, higher-order effects do not provide a way of\u0000circumventing the bound.","PeriodicalId":501113,"journal":{"name":"arXiv - MATH - Differential Geometry","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142199038","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0