An existence theorem of conformal scalar-flat metrics on manifolds with boundary

Details An existence theorem of conformal scalar-flat metrics on manifolds with boundary An existence theorem of conformal scalar-flat metrics on manifolds with boundary

2009-07-04

arxiv.org/abs/0907.0798v1

Pacific J. Math. 248(1) , 1-22 (2010)

Mathematics

Differential Geometry

22 pages

Scientific paper

10.2140/pjm.2010.248-1

Let (M,g) be a compact Riemannian manifold with boundary. This paper
addresses the Yamabe-type problem of finding a conformal scalar-flat metric on
M, which has the boundary as a constant mean curvature hypersurface. When the
boundary is umbilic, we prove an existence theorem that finishes some remaining
cases of this problem.

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