arXiv: Differential Geometry最新文献

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Affine connections on singular warped products 奇异翘曲积上的仿射连接
arXiv: Differential Geometry Pub Date : 2020-11-23 DOI: 10.1142/S0219887821500766
Yong Wang
{"title":"Affine connections on singular warped products","authors":"Yong Wang","doi":"10.1142/S0219887821500766","DOIUrl":"https://doi.org/10.1142/S0219887821500766","url":null,"abstract":"In this paper, we introduce semi-symmetric metric Koszul forms and semi-symmetric non-metric Koszul forms on singular semi-Riemannian manifolds. Semi-symmetric metric Koszul forms and semi-symmetric non-metric Koszul forms and their curvature of semi-regular warped products are expressed in terms of those of the factor manifolds. We also introduce Koszul forms associated to the almost product structure on singular almost product semi-Riemannian manifolds. Koszul forms associated to the almost product structure and their curvature of semi-regular almost product warped products are expressed in terms of those of the factor manifolds. Furthermore, we generalize the results in cite{St2} to singular multiply warped products.","PeriodicalId":8430,"journal":{"name":"arXiv: Differential Geometry","volume":"18 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89586655","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: 1
Existence and uniqueness of inhomogeneous ruled hypersurfaces with shape operator of constant norm in the complex hyperbolic space 复双曲空间中具有常范数形状算子的非齐次直纹超曲面的存在唯一性
arXiv: Differential Geometry Pub Date : 2020-11-17 DOI: 10.1142/S0129167X2150049X
M. Domínguez-Vázquez, Olga Perez-Barral
{"title":"Existence and uniqueness of inhomogeneous ruled hypersurfaces with shape operator of constant norm in the complex hyperbolic space","authors":"M. Domínguez-Vázquez, Olga Perez-Barral","doi":"10.1142/S0129167X2150049X","DOIUrl":"https://doi.org/10.1142/S0129167X2150049X","url":null,"abstract":"We complete the classification of ruled real hypersurfaces with shape operator of constant norm in nonflat complex space forms by showing the existence of a unique inhomogeneous example in the complex hyperbolic space.","PeriodicalId":8430,"journal":{"name":"arXiv: Differential Geometry","volume":"2014 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87748892","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: 1
Comparison of Steklov eigenvalues and Laplacian eigenvalues on graphs 图上Steklov特征值与Laplacian特征值的比较
arXiv: Differential Geometry Pub Date : 2020-10-27 DOI: 10.1090/proc/15866
Yongjie Shi, Chengjie Yu
{"title":"Comparison of Steklov eigenvalues and Laplacian eigenvalues on graphs","authors":"Yongjie Shi, Chengjie Yu","doi":"10.1090/proc/15866","DOIUrl":"https://doi.org/10.1090/proc/15866","url":null,"abstract":"In this paper, we obtain a comparison of Steklov eigenvalues and Laplacian eigenvalues on graphs and discuss its rigidity and some of its applications.","PeriodicalId":8430,"journal":{"name":"arXiv: Differential Geometry","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86497449","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: 8
Lower bounds for the first eigenvalue of the Laplacian on Kähler manifolds Kähler流形上拉普拉斯算子第一个特征值的下界
arXiv: Differential Geometry Pub Date : 2020-10-24 DOI: 10.1090/tran/8434
Xiaolong Li, Kui Wang
{"title":"Lower bounds for the first eigenvalue of the Laplacian on Kähler manifolds","authors":"Xiaolong Li, Kui Wang","doi":"10.1090/tran/8434","DOIUrl":"https://doi.org/10.1090/tran/8434","url":null,"abstract":"We establish lower bound for the first nonzero eigenvalue of the Laplacian on a closed K\"ahler manifold in terms of dimension, diameter, and lower bounds of holomorphic sectional curvature and orthogonal Ricci curvature. On compact K\"ahler manifolds with boundary, we prove lower bounds for the first nonzero Neumann or Dirichlet eigenvalue in terms of geometric data. Our results are K\"ahler analogues of well-known results for Riemannian manifolds.","PeriodicalId":8430,"journal":{"name":"arXiv: Differential Geometry","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78915854","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: 6
Metric rigidity of Kähler manifolds with lower Ricci bounds and almost maximal volume 具有下里奇界和几乎最大体积的Kähler流形的度量刚度
arXiv: Differential Geometry Pub Date : 2020-10-21 DOI: 10.1090/PROC/15473
V. Datar, H. Seshadri, Jian Song
{"title":"Metric rigidity of Kähler manifolds with lower Ricci bounds and almost maximal volume","authors":"V. Datar, H. Seshadri, Jian Song","doi":"10.1090/PROC/15473","DOIUrl":"https://doi.org/10.1090/PROC/15473","url":null,"abstract":"In this short note we prove that a Kahler manifold with lower Ricci curvature bound and almost maximal volume is Gromov-Hausdorff close to the projective space with the Fubini-Study metric. This is done by combining the recent results of Kewei Zhang and Yuchen Liu on holomorphic rigidity of such Kahler manifolds with the structure theorem of Tian-Wang for almost Einstein manifolds. This can be regarded as the complex analog of the result on Colding on the shape of Riemannian manifolds with almost maximal volume","PeriodicalId":8430,"journal":{"name":"arXiv: Differential Geometry","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82032243","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
Growth estimates for generalized harmonic forms on noncompact manifolds with geometric applications 具有几何应用的非紧流形上广义调和形式的增长估计
arXiv: Differential Geometry Pub Date : 2020-10-20 DOI: 10.1090/conm/756/15215
S. Wei
{"title":"Growth estimates for generalized harmonic\u0000 forms on noncompact manifolds with geometric\u0000 applications","authors":"S. Wei","doi":"10.1090/conm/756/15215","DOIUrl":"https://doi.org/10.1090/conm/756/15215","url":null,"abstract":"We introduce Condition W $,$(1.2) for a smooth differential form $omega$ on a complete noncompact Riemannian manifold $M$. We prove that $omega$ is a harmonic form on $M$ if and only if $omega$ is both closed and co-closed on $M, ,$ where $omega$ has $2$-balanced growth either for $q=2$, or for $1 < q(ne 2) < 3, $ with $omega$ satisfying Condition W $,$(1.2). In particular, every $L^2$ harmonic form, or every $L^q$ harmonic form, $1<q(ne 2)<3, $ satisfying Condition W $,$(1.2) is both closed and co-closed (cf. Theorem 1.1). This generalizes the work of A. Andreotti and E. Vesentini [AV] for every $L^2$ harmonic form $omega, .$ In extending $omega$ in $L^2$ to $L^q$, for $q ne 2$, Condition W $,$(1.2) has to be imposed due to counter-examples of D. Alexandru-Rugina$big($ [AR] p. 81, Remarque 3$big).$ We then study nonlinear partial differential inequalities for differential forms $ langleomega, Delta omegarangle ge 0, $ in which solutions $omega$ can be viewed as generalized harmonic forms. We prove that under the same growth assumption on $omega, $ (as in Theorem 1.1, or 1.2, or 1.3), the following six statements: (i) $langleomega, Delta omegarangle ge 0, ,$ (ii) $Delta omega = 0, ,$ $($iii$)$$quad d, omega = d^{star}omega = 0, ,$ (iv) $langle star, omega, Delta star, omegarangle ge 0, ,$ (v) $Delta star, omega = 0, ,$ and (vi) $d, star, omega = d^{star} star, omega = 0, $ are equivalent (cf. Theorem 4.1). We also study As geometric applications, we employ the theory in [DW] and [W3], solve constant Dirichlet problems for generalized harmonic $1$-forms and $F$-harmomic maps (cf. Theorems 10.3 and 10.2), derive monotonicity formulas for $2$-balanced solutions, and vanishing theorems for $2$-moderate solutions of $langleomega, Delta omegarangle ge 0, $ on $M$ (cf. Theorem 8.2 and Theorem 9.3).","PeriodicalId":8430,"journal":{"name":"arXiv: Differential Geometry","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84402831","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: 3
The Limit of The Inverse Mean Curvature Flow on a Torus 环面上逆平均曲率流的极限
arXiv: Differential Geometry Pub Date : 2020-10-20 DOI: 10.1090/proc/15812
Brian Harvie
{"title":"The Limit of The Inverse Mean Curvature Flow on a Torus","authors":"Brian Harvie","doi":"10.1090/proc/15812","DOIUrl":"https://doi.org/10.1090/proc/15812","url":null,"abstract":"For an $H>0$ rotationally symmetric embedded torus $N_{0} subset mathbb{R}^{3}$, evolved by Inverse Mean Curvature Flow, we show that the total curvature $|A|$ remains bounded up to the singular time $T_{max}$. We then show convergence of the $N_{t}$ to a $C^{1}$ rotationally symmetric embedded torus $N_{T_{max}}$ as $t rightarrow T_{max}$ without rescaling. Later, we observe a scale-invariant $L^{2}$ energy estimate on any embedded solution of the flow in $mathbb{R}^{3}$ that may be useful in ruling out curvature blowup near singularities in general.","PeriodicalId":8430,"journal":{"name":"arXiv: Differential Geometry","volume":"165 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78018552","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
Non-Einstein relative Yamabe metrics 非爱因斯坦的相对Yamabe度量
arXiv: Differential Geometry Pub Date : 2020-10-12 DOI: 10.2996/kmj44202
Shota Hamanaka
{"title":"Non-Einstein relative Yamabe metrics","authors":"Shota Hamanaka","doi":"10.2996/kmj44202","DOIUrl":"https://doi.org/10.2996/kmj44202","url":null,"abstract":"In this paper, we give a sufficient condition for a positive constant scalar curvature metric on a manifold with boundary to be a relative Yamabe metric, which is a natural relative version of the classical Yamabe metric. We also give examples of non-Einstein relative Yamabe metrics with positive scalar curvature.","PeriodicalId":8430,"journal":{"name":"arXiv: Differential Geometry","volume":"187 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74426428","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
О гамильтоновой минимальностиизотропных неоднородныхторов в $mathbb H^n$ и $mathbb Cmathrm P^{2n+1}$ 关于哈密顿минимальностиизотропннеоднородныхтор美元/ mathbb H ^ n美元和美元 mathbb C mathrm P ^ {2n + 1}美元
arXiv: Differential Geometry Pub Date : 2020-10-06 DOI: 10.4213/MZM12475
М А Овчаренко, Mikhail Aleksandrovich Ovcharenko
{"title":"О гамильтоновой минимальностиизотропных неоднородных\u0000торов в $mathbb H^n$ и $mathbb Cmathrm P^{2n+1}$","authors":"М А Овчаренко, Mikhail Aleksandrovich Ovcharenko","doi":"10.4213/MZM12475","DOIUrl":"https://doi.org/10.4213/MZM12475","url":null,"abstract":"We construct a family of flat isotropic non-homogeneous tori in $mathbb{H}^n$ and $mathbb{C} mathrm{P}^{2n+1}$ and find necessary and sufficient conditions for their Hamiltonian minimality.","PeriodicalId":8430,"journal":{"name":"arXiv: Differential Geometry","volume":"19 1","pages":"119-129"},"PeriodicalIF":0.0,"publicationDate":"2020-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73232328","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
Metrics of Horowitz–Myers type with the negative constant scalar curvature 负常数标量曲率的Horowitz-Myers型度量
arXiv: Differential Geometry Pub Date : 2020-10-05 DOI: 10.1063/5.0032241
Zhuobin Liang, Xiao Zhang
{"title":"Metrics of Horowitz–Myers type with the negative constant scalar curvature","authors":"Zhuobin Liang, Xiao Zhang","doi":"10.1063/5.0032241","DOIUrl":"https://doi.org/10.1063/5.0032241","url":null,"abstract":"We construct a one-parameter family of complete metrics of Horowitz-Myers type with the negative constant scalar curvature. We also verify a positive energy conjecture of Horowitz-Myers for these metrics.","PeriodicalId":8430,"journal":{"name":"arXiv: Differential Geometry","volume":"36 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77585497","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: 2
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