Journal of Differential Geometry最新文献_第7页

Homogenization of random quasiconformal mappings and random Delauney triangulations 随机拟共形映射的同构与随机Delauney三角剖分

IF 2.5 1区数学

Journal of Differential Geometry Pub Date : 2019-05-20 DOI: 10.4310/jdg/1689262063

O. Ivrii, V. Marković

引用次数: 1

On O’Hara knot energies I: Regularity for critical knots 论O 'Hara结能I:临界结的规律性

IF 2.5 1区数学

Journal of Differential Geometry Pub Date : 2019-05-15 DOI: 10.4310/jdg/1664378616

S. Blatt, P. Reiter, A. Schikorra

引用次数: 8

On the Index of Willmore spheres 关于Willmore球的指数

IF 2.5 1区数学

Journal of Differential Geometry Pub Date : 2019-05-10 DOI: 10.4310/jdg/1685121319

J. Hirsch, E. Mader-Baumdicker

引用次数: 3

Generalized square knots and homotopy $4$-spheres 广义方结与同伦球

IF 2.5 1区数学

Journal of Differential Geometry Pub Date : 2019-04-17 DOI: 10.4310/jdg/1668186788

J. Meier, Alexander Zupan

{"title":"Generalized square knots and homotopy $4$-spheres","authors":"J. Meier, Alexander Zupan","doi":"10.4310/jdg/1668186788","DOIUrl":"https://doi.org/10.4310/jdg/1668186788","url":null,"abstract":"The purpose of this paper is to study geometrically simply-connected homotopy 4-spheres by analyzing $n$-component links with a Dehn surgery realizing $#^n(S^1times S^2)$. We call such links $n$R-links. Our main result is that a homotopy 4-sphere that can be built without 1-handles and with only two 2-handles is diffeomorphic to the standard 4-sphere in the special case that one of the 2-handles is attached along a knot of the form $Q_{p,q} = T_{p,q}#T_{-p,q}$, which we call a generalized square knot. This theorem subsumes prior results of Akbulut and Gompf. \u0000Along the way, we use thin position techniques from Heegaard theory to give a characterization of 2R-links in which one component is a fibered knot, showing that the second component can be converted via trivial handle additions and handleslides to a derivative link contained in the fiber surface. We invoke a theorem of Casson and Gordon and the Equivariant Loop Theorem to classify handlebody-extensions for the closed monodromy of a generalized square knot $Q_{p,q}$. As a consequence, we produce large families, for all even $n$, of $n$R-links that are potential counterexamples to the Generalized Property R Conjecture. We also obtain related classification statements for fibered, homotopy-ribbon disks bounded by generalized square knots.","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":" ","pages":""},"PeriodicalIF":2.5,"publicationDate":"2019-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48464413","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 10

Scherk-like translators for mean curvature flow 平均曲率流的Scherk-like翻译器

IF 2.5 1区数学

Journal of Differential Geometry Pub Date : 2019-03-11 DOI: 10.4310/jdg/1675712995

D. Hoffman, F. Mart'in, B. White

引用次数: 22

Kohn–Rossi cohomology and nonexistence of CR morphisms between compact strongly pseudoconvex CR manifolds 紧强伪凸CR流形间的Kohn-Rossi上同调及CR态射的不存在性

IF 2.5 1区数学

Journal of Differential Geometry Pub Date : 2019-03-01 DOI: 10.4310/JDG/1552442610

S. Yau, Huaiqing Zuo

引用次数: 1

Existence of infinitely many minimal hypersurfaces in higher-dimensional closed manifolds with generic metrics 具有一般度量的高维闭流形中无穷多个极小超曲面的存在性

IF 2.5 1区数学

Journal of Differential Geometry Pub Date : 2019-01-24 DOI: 10.4310/jdg/1686931604

Yangyang Li

引用次数: 24

Symmetries of exotic negatively curved manifolds 奇异负弯曲流形的对称性

IF 2.5 1区数学

Journal of Differential Geometry Pub Date : 2019-01-03 DOI: 10.4310/jdg/1645207478

Mauricio Bustamante, Bena Tshishiku

引用次数: 4

Characterizing symplectic Grassmannians by varieties of minimal rational tangents 用各种最小有理切线来表征辛格拉斯曼

IF 2.5 1区数学

Journal of Differential Geometry Pub Date : 2019-01-02 DOI: 10.4310/jdg/1632506422

Jun-Muk Hwang, Qifeng Li

{"title":"Characterizing symplectic Grassmannians by varieties of minimal rational tangents","authors":"Jun-Muk Hwang, Qifeng Li","doi":"10.4310/jdg/1632506422","DOIUrl":"https://doi.org/10.4310/jdg/1632506422","url":null,"abstract":"We show that if the variety of minimal rational tangents (VMRT) of a uniruled projective manifold at a general point is projectively equivalent to that of a symplectic or an odd-symplectic Grassmannian, the germ of a general minimal rational curve is biholomorphic to the germ of a general line in a presymplectic Grassmannian. As an application, we characterize symplectic and odd-symplectic Grassmannians, among Fano manifolds of Picard number 1, by their VMRT at a general point and prove their rigidity under global K\"ahler deformation. Analogous results for $G/P$ associated with a long root were obtained by Mok and Hong-Hwang a decade ago by using Tanaka theory for parabolic geometries. When $G/P$ is associated with a short root, for which symplectic Grassmannians are most prominent examples, the associated local differential geometric structure is no longer a parabolic geometry and standard machinery of Tanaka theory cannot be applied because of several degenerate features. To overcome the difficulty, we show that Tanaka's method can be generalized to a setting much broader than parabolic geometries, by assuming a pseudo-concavity type condition that certain vector bundles arising from Spencer complexes have no nonzero sections. The pseudo-concavity type condition is checked by exploiting geometry of minimal rational curves.","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":" ","pages":""},"PeriodicalIF":2.5,"publicationDate":"2019-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41571614","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 14

The loop equation for special cubic Hodge integrals 特殊三次Hodge积分的环路方程

IF 2.5 1区数学

Journal of Differential Geometry Pub Date : 2018-11-26 DOI: 10.4310/jdg/1659987894

Si‐Qi Liu, Di Yang, You-jin Zhang, C. Zhou

引用次数: 1