Local existence to the cross curvature flow on 3-manifolds with boundary
Li Ma, Baiyu Liu
TL;DR
This paper establishes the short-time existence of solutions for the cross curvature flow on 3-manifolds with boundary using the DeTurck trick, addressing boundary value problems.
Contribution
It provides the first rigorous proof of local existence for the cross curvature flow with boundary conditions on 3-manifolds.
Findings
Proved short-time existence for Dirichlet boundary conditions.
Proved short-time existence for Neumann boundary conditions.
Applied the DeTurck trick to the cross curvature flow.
Abstract
In this paper, we use the DeTurck trick to study the short-time existence of solutions to the Dirichlet and Newmann boundary problems of the cross curvature flow on 3-manifolds with boundary.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Nonlinear Partial Differential Equations