Static potentials and area minimizing hypersurfaces

Lan Hsuan Huang; Daniel Martin; Pengzi Miao

doi:10.1090/proc/13936

Static potentials and area minimizing hypersurfaces

Lan Hsuan Huang, Daniel Martin, Pengzi Miao

Mathematics

Research output: Contribution to journal › Article

3 Scopus citations

Abstract

We show that if an asymptotically flat manifold with horizon boundary admits a global static potential, then the static potential must be zero on the boundary. We also show that if an asymptotically flat manifold with horizon boundary admits an unbounded static potential in the exterior region, then the manifold must contain a complete non-compact area minimizing hypersurface. Some results related to the Riemannian positive mass theorem, and Bartnik’s quasi-local mass are obtained.

Original language	English (US)
Pages (from-to)	2647-2661
Number of pages	15
Journal	Proceedings of the American Mathematical Society
Volume	146
Issue number	6
DOIs	https://doi.org/10.1090/proc/13936
State	Published - Jan 1 2018

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

Access to Document

10.1090/proc/13936

Fingerprint Dive into the research topics of 'Static potentials and area minimizing hypersurfaces'. Together they form a unique fingerprint.

Cite this

Huang, L. H., Martin, D., & Miao, P. (2018). Static potentials and area minimizing hypersurfaces. Proceedings of the American Mathematical Society, 146(6), 2647-2661. https://doi.org/10.1090/proc/13936

@article{e165d830742e4befb58dff0ffcbba82b,

title = "Static potentials and area minimizing hypersurfaces",

abstract = "We show that if an asymptotically flat manifold with horizon boundary admits a global static potential, then the static potential must be zero on the boundary. We also show that if an asymptotically flat manifold with horizon boundary admits an unbounded static potential in the exterior region, then the manifold must contain a complete non-compact area minimizing hypersurface. Some results related to the Riemannian positive mass theorem, and Bartnik{\textquoteright}s quasi-local mass are obtained.",

author = "Huang, {Lan Hsuan} and Daniel Martin and Pengzi Miao",

year = "2018",

month = jan,

day = "1",

doi = "10.1090/proc/13936",

language = "English (US)",

volume = "146",

pages = "2647--2661",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "6",

}

TY - JOUR

T1 - Static potentials and area minimizing hypersurfaces

AU - Huang, Lan Hsuan

AU - Martin, Daniel

AU - Miao, Pengzi

PY - 2018/1/1

Y1 - 2018/1/1

N2 - We show that if an asymptotically flat manifold with horizon boundary admits a global static potential, then the static potential must be zero on the boundary. We also show that if an asymptotically flat manifold with horizon boundary admits an unbounded static potential in the exterior region, then the manifold must contain a complete non-compact area minimizing hypersurface. Some results related to the Riemannian positive mass theorem, and Bartnik’s quasi-local mass are obtained.

AB - We show that if an asymptotically flat manifold with horizon boundary admits a global static potential, then the static potential must be zero on the boundary. We also show that if an asymptotically flat manifold with horizon boundary admits an unbounded static potential in the exterior region, then the manifold must contain a complete non-compact area minimizing hypersurface. Some results related to the Riemannian positive mass theorem, and Bartnik’s quasi-local mass are obtained.

UR - http://www.scopus.com/inward/record.url?scp=85044364157&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85044364157&partnerID=8YFLogxK

U2 - 10.1090/proc/13936

DO - 10.1090/proc/13936

M3 - Article

AN - SCOPUS:85044364157

VL - 146

SP - 2647

EP - 2661

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 6

ER -