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Strict stability of calibrated cones 校准锥的严格稳定性
arXiv - MATH - Differential Geometry Pub Date : 2024-09-09 DOI: arxiv-2409.06094
Bryan Dimler, Jooho Lee
{"title":"Strict stability of calibrated cones","authors":"Bryan Dimler, Jooho Lee","doi":"arxiv-2409.06094","DOIUrl":"https://doi.org/arxiv-2409.06094","url":null,"abstract":"We study the strict stability of calibrated cones with an isolated\u0000singularity. For special Lagrangian cones and coassociative cones, we prove the\u0000strict stability. In the complex case, we give non-strictly stable examples.","PeriodicalId":501113,"journal":{"name":"arXiv - MATH - Differential Geometry","volume":"18 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142198980","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
On isoparametric foliations of complex and quaternionic projective spaces 论复数和四元投影空间的等参数叶形
arXiv - MATH - Differential Geometry Pub Date : 2024-09-09 DOI: arxiv-2409.06032
Miguel Dominguez-Vazquez, Andreas Kollross
{"title":"On isoparametric foliations of complex and quaternionic projective spaces","authors":"Miguel Dominguez-Vazquez, Andreas Kollross","doi":"arxiv-2409.06032","DOIUrl":"https://doi.org/arxiv-2409.06032","url":null,"abstract":"We conclude the classification of isoparametric (or equivalently, polar)\u0000foliations of complex and quaternionic projective spaces. This is done by\u0000investigating the projections of certain inhomogeneous isoparametric foliations\u0000of the 31-sphere under the respective Hopf fibrations, thereby solving the last\u0000remaining open cases.","PeriodicalId":501113,"journal":{"name":"arXiv - MATH - Differential Geometry","volume":"64 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142198981","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
Generic singularities of holomorphic foliations by curves on $mathbb{P}^n$ $mathbb{P}^n$上曲线全形叶状的泛奇点
arXiv - MATH - Differential Geometry Pub Date : 2024-09-09 DOI: arxiv-2409.06052
Sahil Gehlawat, Viêt-Anh Nguyên
{"title":"Generic singularities of holomorphic foliations by curves on $mathbb{P}^n$","authors":"Sahil Gehlawat, Viêt-Anh Nguyên","doi":"arxiv-2409.06052","DOIUrl":"https://doi.org/arxiv-2409.06052","url":null,"abstract":"Let $mathcal{F}_d(mathbb{P}^n)$ be the space of all singular holomorphic\u0000foliations by curves on $mathbb{P}^n$ ($n geq 2$) with degree $d geq 1.$ We\u0000show that there is subset $mathcal{S}_d(mathbb{P}^n)$ of\u0000$mathcal{F}_d(mathbb{P}^n)$ with full Lebesgue measure with the following\u0000properties: 1. for every $mathcal{F} in mathcal{S}_d(mathbb{P}^n),$ all singular\u0000points of $mathcal{F}$ are linearizable hyperbolic. 2. If, moreover, $d geq 2,$ then every $mathcal{F}$ does not possess any\u0000invariant algebraic curve.","PeriodicalId":501113,"journal":{"name":"arXiv - MATH - Differential Geometry","volume":"28 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142199100","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
Universal central extension of the Lie algebra of exact divergence-free vector fields 精确无发散向量场的李代数的通用中心扩展
arXiv - MATH - Differential Geometry Pub Date : 2024-09-08 DOI: arxiv-2409.05182
Bas Janssens, Leonid Ryvkin, Cornelia Vizman
{"title":"Universal central extension of the Lie algebra of exact divergence-free vector fields","authors":"Bas Janssens, Leonid Ryvkin, Cornelia Vizman","doi":"arxiv-2409.05182","DOIUrl":"https://doi.org/arxiv-2409.05182","url":null,"abstract":"We construct the universal central extension of the Lie algebra of exact\u0000divergence-free vector fields, proving a conjecture by Claude Roger from 1995.\u0000The proof relies on the analysis of a Leibniz algebra that underlies these\u0000vector fields. As an application, we construct the universal central extension\u0000of the (infinite-dimensional) Lie group of exact divergence-free\u0000diffeomorphisms of a compact 3-dimensional manifold.","PeriodicalId":501113,"journal":{"name":"arXiv - MATH - Differential Geometry","volume":"70 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142198984","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
Sharp $mathrm{L}^infty$ estimates for fully non-linear elliptic equations on compact complex manifolds 紧凑复流形上全非线性椭圆方程的尖锐 $mathrm{L}^infty$ 估计值
arXiv - MATH - Differential Geometry Pub Date : 2024-09-08 DOI: arxiv-2409.05157
Yuxiang Qiao
{"title":"Sharp $mathrm{L}^infty$ estimates for fully non-linear elliptic equations on compact complex manifolds","authors":"Yuxiang Qiao","doi":"arxiv-2409.05157","DOIUrl":"https://doi.org/arxiv-2409.05157","url":null,"abstract":"We study the sharp $mathrm{L}^infty$ estimates for fully non-linear\u0000elliptic equations on compact complex manifolds. For the case of K\"ahler\u0000manifolds, we prove that the oscillation of any admissible solution to a\u0000degenerate fully non-linear elliptic equation satisfying several structural\u0000conditions can be controlled by the\u0000$mathrm{L}^1(logmathrm{L})^n(loglogmathrm{L})^r(r>n)$ norm of the\u0000right-hand function (in a regularized form). This result improves that of\u0000Guo-Phong-Tong. In addition to their method of comparison with auxiliary\u0000complex Monge-Amp`ere equations, our proof relies on an inequality of\u0000H\"older-Young type and an iteration lemma of De Giorgi type. For the case of\u0000Hermitian manifolds with non-degenerate background metrics, we prove a similar\u0000$mathrm{L}^infty$ estimate which improves that of Guo-Phong. An explicit\u0000example is constucted to show that the $mathrm{L}^infty$ estimates given here\u0000may fail when $rleqslant n-1$. The construction relies on a gluing lemma of\u0000smooth, radial, strictly plurisubharmonic functions.","PeriodicalId":501113,"journal":{"name":"arXiv - MATH - Differential Geometry","volume":"49 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142199025","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
Some estimates on stable minimal hypersurfaces in Euclidean space 关于欧几里得空间稳定最小超曲面的一些估计
arXiv - MATH - Differential Geometry Pub Date : 2024-09-08 DOI: arxiv-2409.04947
Luen-Fai Tam
{"title":"Some estimates on stable minimal hypersurfaces in Euclidean space","authors":"Luen-Fai Tam","doi":"arxiv-2409.04947","DOIUrl":"https://doi.org/arxiv-2409.04947","url":null,"abstract":"We derive some estimates for stable minimal hypersurfaces in $R^{n+1}$. The\u0000estimates are related to recent proofs of Bernstein theorems for complete\u0000stable minimal hypersurfaces in $R^{n+1}$ for $3le nle 5$ by Chodosh-Li,\u0000Chodosh-Li-Minter-Stryker and Mazet. In particular, the estimates indicate that\u0000the methods in their proofs may not work for $n=6$, which is observed also by\u0000Antonelli-Xu. The method of derivation in this work might also be applied to\u0000other problems.","PeriodicalId":501113,"journal":{"name":"arXiv - MATH - Differential Geometry","volume":"28 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142199022","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
A Note on Ricci-pinched three-manifolds 关于里奇夹角三漫游的说明
arXiv - MATH - Differential Geometry Pub Date : 2024-09-08 DOI: arxiv-2409.05078
Luca Benatti, Carlo Mantegazza, Francesca Oronzio, Alessandra Pluda
{"title":"A Note on Ricci-pinched three-manifolds","authors":"Luca Benatti, Carlo Mantegazza, Francesca Oronzio, Alessandra Pluda","doi":"arxiv-2409.05078","DOIUrl":"https://doi.org/arxiv-2409.05078","url":null,"abstract":"Let $(M, g)$ be a complete, connected, non-compact Riemannian $3$-manifold.\u0000Suppose that $(M,g)$ satisfies the Ricci--pinching condition\u0000$mathrm{Ric}geqvarepsilonmathrm{R} g$ for some $varepsilon>0$, where\u0000$mathrm{Ric}$ and $mathrm{R}$ are the Ricci tensor and scalar curvature,\u0000respectively. In this short note, we give an alternative proof based on\u0000potential theory of the fact that if $(M,g)$ has Euclidean volume growth, then\u0000it is flat. Deruelle-Schulze-Simon and by Huisken-K\"{o}rber have already shown\u0000this result and together with the contributions by Lott and Lee-Topping led to\u0000a proof of the so-called Hamilton's pinching conjecture.","PeriodicalId":501113,"journal":{"name":"arXiv - MATH - Differential Geometry","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142199020","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
Generalized paracomplex structures on generalized reflector spaces 广义反射空间上的广义准复数结构
arXiv - MATH - Differential Geometry Pub Date : 2024-09-07 DOI: arxiv-2409.04835
Johann Davidov
{"title":"Generalized paracomplex structures on generalized reflector spaces","authors":"Johann Davidov","doi":"arxiv-2409.04835","DOIUrl":"https://doi.org/arxiv-2409.04835","url":null,"abstract":"Non-trivial examples of generalized paracomplex structures (in the sense of\u0000the generalized geometry `a la Hitchin) are constructed applying the twistor\u0000space construction scheme.","PeriodicalId":501113,"journal":{"name":"arXiv - MATH - Differential Geometry","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142199023","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
The decoupling of moduli about the standard embedding 关于标准嵌入的解耦模量
arXiv - MATH - Differential Geometry Pub Date : 2024-09-06 DOI: arxiv-2409.04350
Beatrice Chisamanga, Jock McOrist, Sebastien Picard, Eirik Eik Svanes
{"title":"The decoupling of moduli about the standard embedding","authors":"Beatrice Chisamanga, Jock McOrist, Sebastien Picard, Eirik Eik Svanes","doi":"arxiv-2409.04350","DOIUrl":"https://doi.org/arxiv-2409.04350","url":null,"abstract":"We study the cohomology of an elliptic differential complex arising from the\u0000infinitesimal moduli of heterotic string theory. We compute these cohomology\u0000groups at the standard embedding, and show that they decompose into a direct\u0000sum of cohomologies. While this is often assumed in the literature, it had not\u0000been explicitly demonstrated. Given a stable gauge bundle over a complex\u0000threefold with trivial canonical bundle and no holomorphic vector fields, we\u0000also show that the Euler characteristic of this differential complex is zero.\u0000This points towards a perfect obstruction theory for the heterotic moduli\u0000problem, at least for the most physically relevant compactifications.","PeriodicalId":501113,"journal":{"name":"arXiv - MATH - Differential Geometry","volume":"82 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142199033","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
Local descriptions of the heterotic SU(3) moduli space 异质 SU(3) 模态空间的局部描述
arXiv - MATH - Differential Geometry Pub Date : 2024-09-06 DOI: arxiv-2409.04382
Hannah de Lázari, Jason D. Lotay, Henrique Sá Earp, Eirik Eik Svanes
{"title":"Local descriptions of the heterotic SU(3) moduli space","authors":"Hannah de Lázari, Jason D. Lotay, Henrique Sá Earp, Eirik Eik Svanes","doi":"arxiv-2409.04382","DOIUrl":"https://doi.org/arxiv-2409.04382","url":null,"abstract":"The heterotic $SU(3)$ system, also known as the Hull--Strominger system,\u0000arises from compactifications of heterotic string theory to six dimensions.\u0000This paper investigates the local structure of the moduli space of solutions to\u0000this system on a compact 6-manifold $X$, using a vector bundle $Q=(T^{1,0}X)^*\u0000oplus {End}(E) oplus T^{1,0}X$, where $Eto X$ is the classical gauge bundle\u0000arising in the system. We establish that the moduli space has an expected\u0000dimension of zero. We achieve this by studying the deformation complex\u0000associated to a differential operator $bar{D}$, which emulates a holomorphic\u0000structure on $Q$, and demonstrating an isomorphism between the two cohomology\u0000groups which govern the infinitesimal deformations and obstructions in the\u0000deformation theory for the system. We also provide a Dolbeault-type theorem\u0000linking these cohomology groups to v{C}ech cohomology, a result which might be\u0000of independent interest, as well as potentially valuable for future research.","PeriodicalId":501113,"journal":{"name":"arXiv - MATH - Differential Geometry","volume":"58 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142199027","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
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