THE RIEMANNIAN PENROSE INEQUALITY FOR ASYMPTOTICALLY FLAT MANIFOLDS WITH NON-COMPACT BOUNDARY

被引：0

作者：

Koerber, Thomas ^{[1
]}

机构：

[1] Univ Vienna, Fac Math, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria

来源：

JOURNAL OF DIFFERENTIAL GEOMETRY | 2023年 / 124卷 / 02期

关键词：

MEAN-CURVATURE FLOW; STAR-SHAPED HYPERSURFACES; POSITIVE MASS THEOREM; MINIMAL-SURFACES; REGULARITY; EXISTENCE; TOPOLOGY; PROOF; CONJECTURE;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove the Riemannian Penrose inequality for asymptotically flat manifolds with non-compact boundary whose asymptotic region is modeled on a half-space. To this end, we develop the theory of weak free boundary inverse mean curvature flow further and establish the monotonicity of a modified Hawking mass along this flow. Our result also implies a non-optimal Penrose inequality for asymptotically flat support surfaces in R3 conjectured by G. Huisken.

引用

页码：317 / 379

页数：63

共 50 条

[1] A positive mass theorem for asymptotically flat manifolds with a non-compact boundary
Almaraz, Sergio
Barbosa, Ezequiel
de Lima, Levi Lopes
[J]. COMMUNICATIONS IN ANALYSIS AND GEOMETRY, 2016, 24 (04) : 673 - 715
[2] A Penrose-like inequality for the mass of Riemannian asymptotically flat manifolds
Herzlich, M
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1997, 188 (01) : 121 - 133
[3] A Penrose-like Inequality for the Mass of Riemannian Asymptotically Flat Manifolds
Marc Herzlich
[J]. Communications in Mathematical Physics, 1997, 188 : 121 - 133
[4] On the rigidity of Riemannian–Penrose inequality for asymptotically flat 3-manifolds with corners
Yuguang Shi
Wenlong Wang
Haobin Yu
[J]. Mathematische Zeitschrift, 2019, 291 : 569 - 589
[5] On the rigidity of Riemannian-Penrose inequality for asymptotically flat 3-manifolds with corners
Shi, Yuguang
Wang, Wenlong
Yu, Haobin
[J]. MATHEMATISCHE ZEITSCHRIFT, 2019, 291 (1-2) : 569 - 589
[6] Existence of a closed geodesic on non-compact Riemannian manifolds with boundary
Bartolo, R
Germinario, A
Sánchez, M
[J]. ADVANCED NONLINEAR STUDIES, 2002, 2 (01) : 51 - 69
[7] Doubling of Asymptotically Flat Half-spaces and the Riemannian Penrose Inequality
Eichmair, Michael
Koerber, Thomas
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2023, 400 (3) : 1823 - 1860
[8] Doubling of Asymptotically Flat Half-spaces and the Riemannian Penrose Inequality
Michael Eichmair
Thomas Koerber
[J]. Communications in Mathematical Physics, 2023, 400 : 1823 - 1860
[9] Geodesic nets on non-compact Riemannian manifolds
Chambers, Gregory R.
Liokumovich, Yevgeny
Nabutovsky, Alexander
Rotman, Regina
[J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2023, 2023 (799): : 287 - 303
[10] CLOSED GEODESICS ON NON-COMPACT RIEMANNIAN MANIFOLDS
THORBERGSSON, G
[J]. MATHEMATISCHE ZEITSCHRIFT, 1978, 159 (03) : 249 - 258

← 1 2 3 4 5 →