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The dilogarithm and abelian Chern–Simons 二重数与阿贝尔陈-西蒙斯
IF 2.5 1区 数学
Journal of Differential Geometry Pub Date : 2020-06-22 DOI: 10.4310/jdg/1680883577
D. Freed, A. Neitzke
{"title":"The dilogarithm and abelian Chern–Simons","authors":"D. Freed, A. Neitzke","doi":"10.4310/jdg/1680883577","DOIUrl":"https://doi.org/10.4310/jdg/1680883577","url":null,"abstract":"We construct the (enhanced Rogers) dilogarithm function from the spin Chern-Simons invariant of C*-connections. This leads to geometric proofs of basic dilogarithm identities and a geometric context for other properties, such as the branching structure.","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":" ","pages":""},"PeriodicalIF":2.5,"publicationDate":"2020-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46061039","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: 0
Expanding Kähler–Ricci solitons coming out of Kähler cones 膨胀的Kähler-Ricci孤子从Kähler锥体中出来
IF 2.5 1区 数学
Journal of Differential Geometry Pub Date : 2020-06-01 DOI: 10.4310/jdg/1589853627
Ronan J. Conlon, Alix Deruelle
{"title":"Expanding Kähler–Ricci solitons coming out of Kähler cones","authors":"Ronan J. Conlon, Alix Deruelle","doi":"10.4310/jdg/1589853627","DOIUrl":"https://doi.org/10.4310/jdg/1589853627","url":null,"abstract":"We give necessary and sufficient conditions for a Kähler equivariant resolution of a Kähler cone, with the resolution satisfying one of a number of auxiliary conditions, to admit a unique asymptotically conical (AC) expanding gradient Kähler-Ricci soliton. In particular, it follows that for any n ∈ N0 and for L a negative line bundle over a compact Kähler manifold D, the total space of the vector bundle L⊕(n+1) admits a unique AC expanding gradient Kähler-Ricci soliton with soliton vector field a positive multiple of the Euler vector field if and only if c1(KD⊗(L)) > 0. This generalises the examples already known in the literature. We further prove a general uniqueness result and show that the space of certain AC expanding gradient Kähler-Ricci solitons on C with positive curvature operator on (1, 1)-forms is path-connected.","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":" ","pages":""},"PeriodicalIF":2.5,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47952089","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: 17
Morse inequalities for the area functional 区域泛函的Morse不等式
IF 2.5 1区 数学
Journal of Differential Geometry Pub Date : 2020-03-03 DOI: 10.4310/jdg/1685121320
F. C. Marques, Rafael Montezuma, A. Neves
{"title":"Morse inequalities for the area functional","authors":"F. C. Marques, Rafael Montezuma, A. Neves","doi":"10.4310/jdg/1685121320","DOIUrl":"https://doi.org/10.4310/jdg/1685121320","url":null,"abstract":"In this article we prove the strong Morse inequalities for the area functional in codimension one, assuming that the ambient dimension satisfies $3 leq (n + 1) leq 7$, in both the closed and the boundary cases.","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":" ","pages":""},"PeriodicalIF":2.5,"publicationDate":"2020-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45701916","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
The Weyl problem in warped product spaces 扭曲积空间中的Weyl问题
IF 2.5 1区 数学
Journal of Differential Geometry Pub Date : 2020-02-01 DOI: 10.4310/jdg/1580526016
Chunhe Li, Zhizhang Wang
{"title":"The Weyl problem in warped product spaces","authors":"Chunhe Li, Zhizhang Wang","doi":"10.4310/jdg/1580526016","DOIUrl":"https://doi.org/10.4310/jdg/1580526016","url":null,"abstract":"In this paper, we discuss the Weyl problem in warped product spaces. We apply the method of continuity and prove the openness of the Weyl problem. A counterexample is constructed to show that the isometric embedding of the sphere with canonical metric is not unique up to an isometry if the ambient warped product space is not a space form. Then, we study the rigidity of the standard sphere if we fixed its geometric center in the ambient space. Finally, we discuss a Shi-Tam type of inequality for the Schwarzschild manifold as an application of our findings.","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":"114 1","pages":"243-304"},"PeriodicalIF":2.5,"publicationDate":"2020-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47159225","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: 13
Cohomology of contact loci 接触位点的同调
IF 2.5 1区 数学
Journal of Differential Geometry Pub Date : 2019-11-19 DOI: 10.4310/jdg/1649953456
Nero Budur, J. F. Bobadilla, Q. Lê, H. Nguyen
{"title":"Cohomology of contact loci","authors":"Nero Budur, J. F. Bobadilla, Q. Lê, H. Nguyen","doi":"10.4310/jdg/1649953456","DOIUrl":"https://doi.org/10.4310/jdg/1649953456","url":null,"abstract":"We construct a spectral sequence converging to the cohomology with compact support of the m-th contact locus of a complex polynomial. The first page is explicitly described in terms of a log resolution and coincides with the first page of McLean's spectral sequence converging to the Floer cohomology of the m-th iterate of the monodromy, when the polynomial has an isolated singularity. Inspired by this connection, we conjecture that if two germs of holomorphic functions are embedded topologically equivalent, then the Milnor fibers of the their tangent cones are homotopy equivalent.","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":" ","pages":""},"PeriodicalIF":2.5,"publicationDate":"2019-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43882131","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: 8
Infinite energy equivariant harmonic maps, domination, and anti-de Sitter $3$-manifolds 无限能量等变谐波映射，支配和反德西特$3 -流形
IF 2.5 1区 数学
Journal of Differential Geometry Pub Date : 2019-11-16 DOI: 10.4310/jdg/1689262064
Nathaniel Sagman
{"title":"Infinite energy equivariant harmonic maps, domination, and anti-de Sitter $3$-manifolds","authors":"Nathaniel Sagman","doi":"10.4310/jdg/1689262064","DOIUrl":"https://doi.org/10.4310/jdg/1689262064","url":null,"abstract":"We generalize a well-known existence and uniqueness result for equivariant harmonic maps due to Corlette, Donaldson, and Labourie to a non-compact infinite energy setting and analyze the asymptotic behaviour of the harmonic maps. When the relevant representation is Fuchsian and has hyperbolic monodromy, our construction recovers a family of harmonic maps originally studied by Wolf. \u0000We employ these maps to solve a domination problem for representations. In particular, following ideas laid out by Deroin-Tholozan, we prove that any representation from a finitely generated free group to the isometry group of a CAT$(-1)$ Hadamard manifold is strictly dominated in length spectrum by a large collection of Fuchsian ones. As an intermediate step in the proof, we obtain a result of independent interest: parametrizations of certain Teichm{\"u}ller spaces by holomorphic quadratic differentials. The main consequence of the domination result is the existence of a new collection of anti-de Sitter $3$-manifolds. We also present an application to the theory of minimal immersions into the Grassmanian of timelike planes in $mathbb{R}^{2,2}$.","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":" ","pages":""},"PeriodicalIF":2.5,"publicationDate":"2019-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43155045","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: 4
Convex $mathbb{RP}^2$ structures and cubic differentials under neck separation 凸$mathbb｛RP｝^2$结构和颈分离下的三次微分
IF 2.5 1区 数学
Journal of Differential Geometry Pub Date : 2019-10-01 DOI: 10.4310/jdg/1571882429
John C. Loftin
{"title":"Convex $mathbb{RP}^2$ structures and cubic differentials under neck separation","authors":"John C. Loftin","doi":"10.4310/jdg/1571882429","DOIUrl":"https://doi.org/10.4310/jdg/1571882429","url":null,"abstract":"","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":" ","pages":""},"PeriodicalIF":2.5,"publicationDate":"2019-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44757964","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: 4
The Riemannian Penrose inequality for asymptotically flat manifolds with non-compact boundary 非紧边渐近平面流形的黎曼彭罗斯不等式
IF 2.5 1区 数学
Journal of Differential Geometry Pub Date : 2019-09-29 DOI: 10.4310/jdg/1686931603
T. Koerber
{"title":"The Riemannian Penrose inequality for asymptotically flat manifolds with non-compact boundary","authors":"T. Koerber","doi":"10.4310/jdg/1686931603","DOIUrl":"https://doi.org/10.4310/jdg/1686931603","url":null,"abstract":"In this article, we prove the Riemannian Penrose inequality for asymptotically flat manifolds with non-compact boundary whose asymptotic region is modelled on a half-space. Such spaces were initially considered by Almaraz, Barbosa and de Lima in 2014. In order to prove the inequality, we develop a new approximation scheme for the weak free boundary inverse mean curvature flow, introduced by Marquardt in 2012, and establish the monotonicity of a free boundary version of the Hawking mass. Our result also implies a non-optimal Penrose inequality for asymptotically flat support surfaces in $mathbb{R}^3$ and thus sheds some light on a conjecture made by Huisken.","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":" ","pages":""},"PeriodicalIF":2.5,"publicationDate":"2019-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47885229","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: 6
Maximizing Steklov eigenvalues on surfaces 曲面上Steklov特征值的最大化
IF 2.5 1区 数学
Journal of Differential Geometry Pub Date : 2019-09-01 DOI: 10.4310/jdg/1567216955
R. Petrides
{"title":"Maximizing Steklov eigenvalues on surfaces","authors":"R. Petrides","doi":"10.4310/jdg/1567216955","DOIUrl":"https://doi.org/10.4310/jdg/1567216955","url":null,"abstract":"","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":" ","pages":""},"PeriodicalIF":2.5,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4310/jdg/1567216955","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48470351","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: 21
Scalar curvature and harmonic maps to $S^1$ S^1的标量曲率和调和映射
IF 2.5 1区 数学
Journal of Differential Geometry Pub Date : 2019-08-26 DOI: 10.4310/jdg/1669998185
Daniel Stern
{"title":"Scalar curvature and harmonic maps to $S^1$","authors":"Daniel Stern","doi":"10.4310/jdg/1669998185","DOIUrl":"https://doi.org/10.4310/jdg/1669998185","url":null,"abstract":"For a harmonic map $u:M^3to S^1$ on a closed, oriented $3$--manifold, we establish the identity $$2pi int_{thetain S^1}chi(Sigma_{theta})geq frac{1}{2}int_{thetain S^1}int_{Sigma_{theta}}(|du|^{-2}|Hess(u)|^2+R_M)$$ relating the scalar curvature $R_M$ of $M$ to the average Euler characteristic of the level sets $Sigma_{theta}=u^{-1}{theta}$. As our primary application, we extend the Kronheimer--Mrowka characterization of the Thurston norm on $H_2(M;mathbb{Z})$ in terms of $|R_M^-|_{L^2}$ and the harmonic norm to any closed $3$--manifold containing no nonseparating spheres. Additional corollaries include the Bray--Brendle--Neves rigidity theorem for the systolic inequality $(min R_M)sys_2(M)leq 8pi$, and the well--known result of Schoen and Yau that $T^3$ admits no metric of positive scalar curvature.","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":" ","pages":""},"PeriodicalIF":2.5,"publicationDate":"2019-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42654624","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: 55
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