Quasilinear Parabolic Equations and the Ricci Flow on Manifolds with Boundary

Details Quasilinear Parabolic Equations and the Ricci Flow on Manifolds with Boundary Quasilinear Parabolic Equations and the Ricci Flow on Manifolds with Boundary

2010-12-14

arxiv.org/abs/1012.2941v3

Mathematics

Analysis of PDEs

18 pages

Scientific paper

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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