Noncompact 4-manifolds with uniformly positive isotropic curvature

Liang Ming Shen

doi:10.1007/s10114-015-1611-y

Noncompact 4-manifolds with uniformly positive isotropic curvature

Liang Ming Shen^*

^*Corresponding author for this work

Princeton University

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

Abstract

In this paper, we study Ricci flow on noncompact 4-manifolds with uniformly positive isotropic curvature and with no essential imcompressible space form. That means there is positive lower bound of isotropic curvature and bounded geometry. Then by Perelman’s technique, we can analyze the structures of such manifolds.

Original language	English
Pages (from-to)	1391-1414
Number of pages	24
Journal	Acta Mathematica Sinica, English Series
Volume	31
Issue number	9
DOIs	https://doi.org/10.1007/s10114-015-1611-y
State	Published - 8 Sep 2015
Externally published	Yes

Keywords

Ricci flow
isotropic curvature
surgery

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10.1007/s10114-015-1611-y

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title = "Noncompact 4-manifolds with uniformly positive isotropic curvature",

abstract = "In this paper, we study Ricci flow on noncompact 4-manifolds with uniformly positive isotropic curvature and with no essential imcompressible space form. That means there is positive lower bound of isotropic curvature and bounded geometry. Then by Perelman{\textquoteright}s technique, we can analyze the structures of such manifolds.",

keywords = "Ricci flow, isotropic curvature, surgery",

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note = "Publisher Copyright: {\textcopyright} 2015, Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg.",

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doi = "10.1007/s10114-015-1611-y",

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AB - In this paper, we study Ricci flow on noncompact 4-manifolds with uniformly positive isotropic curvature and with no essential imcompressible space form. That means there is positive lower bound of isotropic curvature and bounded geometry. Then by Perelman’s technique, we can analyze the structures of such manifolds.

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KW - isotropic curvature

KW - surgery

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JF - Acta Mathematica Sinica, English Series

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Noncompact 4-manifolds with uniformly positive isotropic curvature

Abstract

Keywords

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