Short-time existence of solutions to the cross curvature flow on 3-manifolds

John A. Buckland

doi:10.1090/S0002-9939-05-08204-3

Short-time existence of solutions to the cross curvature flow on 3-manifolds

John A. Buckland^*

^*Corresponding author for this work

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

16 Citations (Scopus)

Abstract

Given a compact 3-manifold with an initial Riemannian metric of positive (or negative) sectional curvature, we prove the short-time existence of a solution to the cross curvature flow. This is achieved using an idea first introduced by DeTurck (1983) in his work establishing the short-time existence of solutions to the Ricci flow.

Original language	English
Pages (from-to)	1803-1807
Number of pages	5
Journal	Proceedings of the American Mathematical Society
Volume	134
Issue number	6
DOIs	https://doi.org/10.1090/S0002-9939-05-08204-3
Publication status	Published - Jun 2006

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title = "Short-time existence of solutions to the cross curvature flow on 3-manifolds",

abstract = "Given a compact 3-manifold with an initial Riemannian metric of positive (or negative) sectional curvature, we prove the short-time existence of a solution to the cross curvature flow. This is achieved using an idea first introduced by DeTurck (1983) in his work establishing the short-time existence of solutions to the Ricci flow.",

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AB - Given a compact 3-manifold with an initial Riemannian metric of positive (or negative) sectional curvature, we prove the short-time existence of a solution to the cross curvature flow. This is achieved using an idea first introduced by DeTurck (1983) in his work establishing the short-time existence of solutions to the Ricci flow.

KW - Curvature flow

KW - Nonlinear evolution equations

KW - Short-time existence

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U2 - 10.1090/S0002-9939-05-08204-3

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SP - 1803

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JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

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ER -

Short-time existence of solutions to the cross curvature flow on 3-manifolds

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