Szu-yu Sophie Chen
Published 2009-12-07, updated 2010-04-08Version 2
In 1992, motivated by Riemann mapping theorem, Escobar considered a version of Yamabe problem on manifolds of dimension n greater than 2 with boundary. The problem consists in finding a conformal metric such that the scalar curvature is zero and the mean curvature is constant on the boundary. By using a local test function construction, we are able to seattle the most cases left by Escobar's and Marques's works. Moreover, we reduce the remaining case to the positive mass theorem. In this proof, we use the method developed in previous works by Brendle and by Brendle and the author.
Comments: 27 pages, title changed, introduction expanded
Vertical Ends of Constant Mean Curvature H=1/2 in H^2\times R
Constant mean curvature $k$-noids in homogeneous manifolds
Surfaces of annulus type with constant mean curvature in Lorentz-Minkowski space
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