Rigidity Theorems for Diameter Estimates of Compact Manifold with Boundary
-
Altmetric Citations
Description
Let (N,g) be an n-dimensional complete Riemannian manifold with nonempty boundary ∂N. Assume that the Ricci curvature of (N,g) has a negative lower bound Ric≥−(n−1)c2 for some c>0, and the mean curvature of the boundary ∂N satisfies H≥(n−1)c0>(n−1)c for some c0>c>0. Then a known result (cf. [12]) says that supx∈Nd(x,∂N)≤1ccoth−1c0c. In this paper, we prove the rigidity result that if N is compact, then the equality holds if and only if (N,g) is isometric to the geodesic ball of radius...[Show more]
dc.contributor.author | Li, Haizhong | |
---|---|---|
dc.contributor.author | Wei, Yong | |
dc.date.accessioned | 2019-11-25T23:40:07Z | |
dc.identifier.issn | 1073-7928 | |
dc.identifier.uri | http://hdl.handle.net/1885/186628 | |
dc.description.abstract | Let (N,g) be an n-dimensional complete Riemannian manifold with nonempty boundary ∂N. Assume that the Ricci curvature of (N,g) has a negative lower bound Ric≥−(n−1)c2 for some c>0, and the mean curvature of the boundary ∂N satisfies H≥(n−1)c0>(n−1)c for some c0>c>0. Then a known result (cf. [12]) says that supx∈Nd(x,∂N)≤1ccoth−1c0c. In this paper, we prove the rigidity result that if N is compact, then the equality holds if and only if (N,g) is isometric to the geodesic ball of radius 1ccoth−1c0c in an n-dimensional hyperbolic space Hn(−c2) of constant sectional curvature −c2. Moreover, we prove an analogous result for manifold with m-Bakry–Émery Ricci curvature bounded below by a negative constant. | |
dc.description.sponsorship | The research of the authors was supported by NSFC No. 11271214. | |
dc.format.mimetype | application/pdf | |
dc.language.iso | en_AU | |
dc.publisher | Duke University Press | |
dc.rights | © 2014 The Author(s) | |
dc.source | International Mathematics Research Notices | |
dc.title | Rigidity Theorems for Diameter Estimates of Compact Manifold with Boundary | |
dc.type | Journal article | |
local.description.notes | Imported from ARIES | |
local.identifier.citationvolume | 2015 | |
dcterms.dateAccepted | 2014-03-10 | |
dc.date.issued | 2014-04-02 | |
local.identifier.absfor | 010102 - Algebraic and Differential Geometry | |
local.identifier.ariespublication | u5013521xPUB47 | |
local.publisher.url | https://academic.oup.com | |
local.type.status | Published Version | |
local.contributor.affiliation | Li, Haizhong, Tsinghua University | |
local.contributor.affiliation | Wei, Yong, Tsinghua University | |
local.description.embargo | 2037-12-31 | |
local.bibliographicCitation.issue | 11 | |
local.bibliographicCitation.startpage | 3651 | |
local.bibliographicCitation.lastpage | 3668 | |
local.identifier.doi | 10.1093/imrn/rnu052 | |
local.identifier.absseo | 970101 - Expanding Knowledge in the Mathematical Sciences | |
dc.date.updated | 2019-05-19T08:23:17Z | |
Collections | ANU Research Publications |
Download
File | Description | Size | Format | Image |
---|---|---|---|---|
01_Li_Rigidity_Theorems_for_Diameter_2014.pdf | 195 kB | Adobe PDF | Request a copy |
Items in Open Research are protected by copyright, with all rights reserved, unless otherwise indicated.
Updated: 17 November 2022/ Responsible Officer: University Librarian/ Page Contact: Library Systems & Web Coordinator