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arXiv · 1012.2941

Quasilinear Parabolic Equations and the Ricci Flow on Manifolds with Boundary

Artem Pulemotov
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Abstract

The first part of the paper discusses a second-order quasilinear parabolic equation in a vector bundle over a compact manifold $M$ with boundary $\partial M$. We establish a short-time existence theorem for this equation. The second part of the paper is devoted to the investigation of the Ricci flow on $M$. We propose a new boundary condition for the flow and prove two short-time existence results.

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Artem Pulemotov. 2010-12-14. Quasilinear Parabolic Equations and the Ricci Flow on Manifolds with Boundary. https://arxiv.org/abs/1012.2941

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