Singular angles of weak limiting metrics under certain integral curvature bounds

Qing Chen; Xiuxiong Chen; Weiyong He

doi:10.2140/pjm.2007.231.35

Singular angles of weak limiting metrics under certain integral curvature bounds

Qing Chen
, Xiuxiong Chen
, Weiyong He

Mathematics

Stony Brook University

University of Science and Technology of China

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

Abstract

We prove that a nonvanishing weak limit of Riemannian metrics in surfaces with an integral curvature bound admits only weak cusp singularities. The result is useful toward generalizing classical uniformization theory to surfaces with boundary.

Original language	English
Pages (from-to)	35-49
Number of pages	15
Journal	Pacific Journal of Mathematics
Volume	231
Issue number	1
DOIs	https://doi.org/10.2140/pjm.2007.231.35
State	Published - May 2007

Keywords

Riemannian metric
Singular angle
Weak limit

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10.2140/pjm.2007.231.35

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title = "Singular angles of weak limiting metrics under certain integral curvature bounds",

abstract = "We prove that a nonvanishing weak limit of Riemannian metrics in surfaces with an integral curvature bound admits only weak cusp singularities. The result is useful toward generalizing classical uniformization theory to surfaces with boundary.",

keywords = "Riemannian metric, Singular angle, Weak limit",

author = "Qing Chen and Xiuxiong Chen and Weiyong He",

year = "2007",

month = may,

doi = "10.2140/pjm.2007.231.35",

language = "English",

volume = "231",

pages = "35--49",

journal = "Pacific Journal of Mathematics",

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AU - Chen, Xiuxiong

AU - He, Weiyong

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N2 - We prove that a nonvanishing weak limit of Riemannian metrics in surfaces with an integral curvature bound admits only weak cusp singularities. The result is useful toward generalizing classical uniformization theory to surfaces with boundary.

AB - We prove that a nonvanishing weak limit of Riemannian metrics in surfaces with an integral curvature bound admits only weak cusp singularities. The result is useful toward generalizing classical uniformization theory to surfaces with boundary.

KW - Riemannian metric

KW - Singular angle

KW - Weak limit

UR - https://www.scopus.com/pages/publications/70349775539

U2 - 10.2140/pjm.2007.231.35

DO - 10.2140/pjm.2007.231.35

M3 - Article

SN - 0030-8730

VL - 231

SP - 35

EP - 49

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

IS - 1

ER -

Singular angles of weak limiting metrics under certain integral curvature bounds

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Keywords

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