Interior curvature bounds for spacelike hypersurfaces of prescribed k-th mean curvature

John Urbas

doi:10.4310/CAG.2003.v11.n2.a4

Interior curvature bounds for spacelike hypersurfaces of prescribed k-th mean curvature

John Urbas^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

We derive interior curvature bounds for strictly spacelike hypersurfaces of prescribed k-th mean curvature in Minkowski space analogous to those we derived in previous work on the Euclidean case. The estimates depend on a sufficiently large L^p norm of the mean curvature. Examples similar to those in the Euclidean case show that if k ≥ 3, such curvature bounds are generally false if p is not sufficiently large.

Original language	English
Pages (from-to)	235-261
Number of pages	27
Journal	Communications in Analysis and Geometry
Volume	11
Issue number	2
DOIs	https://doi.org/10.4310/CAG.2003.v11.n2.a4
Publication status	Published - Jun 2003

Access to Document

10.4310/CAG.2003.v11.n2.a4

Cite this

@article{d99b31bb0f724d9b86bf844702b700d8,

title = "Interior curvature bounds for spacelike hypersurfaces of prescribed k-th mean curvature",

abstract = "We derive interior curvature bounds for strictly spacelike hypersurfaces of prescribed k-th mean curvature in Minkowski space analogous to those we derived in previous work on the Euclidean case. The estimates depend on a sufficiently large Lp norm of the mean curvature. Examples similar to those in the Euclidean case show that if k ≥ 3, such curvature bounds are generally false if p is not sufficiently large.",

author = "John Urbas",

year = "2003",

month = jun,

doi = "10.4310/CAG.2003.v11.n2.a4",

language = "English",

volume = "11",

pages = "235--261",

journal = "Communications in Analysis and Geometry",

issn = "1019-8385",

publisher = "International Press of Boston, Inc.",

number = "2",

}

TY - JOUR

T1 - Interior curvature bounds for spacelike hypersurfaces of prescribed k-th mean curvature

AU - Urbas, John

PY - 2003/6

Y1 - 2003/6

N2 - We derive interior curvature bounds for strictly spacelike hypersurfaces of prescribed k-th mean curvature in Minkowski space analogous to those we derived in previous work on the Euclidean case. The estimates depend on a sufficiently large Lp norm of the mean curvature. Examples similar to those in the Euclidean case show that if k ≥ 3, such curvature bounds are generally false if p is not sufficiently large.

AB - We derive interior curvature bounds for strictly spacelike hypersurfaces of prescribed k-th mean curvature in Minkowski space analogous to those we derived in previous work on the Euclidean case. The estimates depend on a sufficiently large Lp norm of the mean curvature. Examples similar to those in the Euclidean case show that if k ≥ 3, such curvature bounds are generally false if p is not sufficiently large.

UR - http://www.scopus.com/inward/record.url?scp=4043062830&partnerID=8YFLogxK

U2 - 10.4310/CAG.2003.v11.n2.a4

DO - 10.4310/CAG.2003.v11.n2.a4

M3 - Article

SN - 1019-8385

VL - 11

SP - 235

EP - 261

JO - Communications in Analysis and Geometry

JF - Communications in Analysis and Geometry

IS - 2

ER -

Interior curvature bounds for spacelike hypersurfaces of prescribed k-th mean curvature

Abstract

Access to Document

Other files and links

Fingerprint

Cite this