The Ricci flow on manifolds with boundary
Abstract
We study the short-time existence and regularity of solutions to a boundary value problem for the Ricci-DeTurck equation on a manifold with boundary. Using this, we prove the short-time existence and uniqueness of the Ricci flow prescribing the mean curvature and conformal class of the boundary, with arbitrary initial data. Finally, we establish that under suitable control of the boundary data the flow exists as long as the ambient curvature and the second fundamental form of the boundary remain bounded.
Keywords
Cite
@article{arxiv.1210.0813,
title = {The Ricci flow on manifolds with boundary},
author = {Panagiotis Gianniotis},
journal= {arXiv preprint arXiv:1210.0813},
year = {2015}
}
Comments
Improved exposition and statement on the control of the existence time of the Ricci flow, and updated/added some references. Also, a new section is added, demonstrating a situation in which the existence time of the Ricci flow (with boundary) with flat initial data and well behaved boundary data may become arbitrarily small