Convergence of the Yamabe flow on manifolds with boundary
by Dai, Dongyan, Ph.D., UNIVERSITY OF CALIFORNIA, SANTA BARBARA, 2008, 111 pages; 3330422

Abstract:

We prove convergence of the Yamabe flow on manifolds with boundary in dimensions 3, 4, and 5, 66tg= r-Rg, under minimal boundary condition, h=0 on6M where R is the scalar curvature of g, r denotes the mean value of R, and h is the mean curvature on the boundary ∂M.

We extend Struwe's compactness result [29] for blow-up limits to manifolds with boundary. Then we apply Brendle's approach [6] to the test function introduced by Escobar [11] and rule out the formation of volume concentration, which leads to the convergence of Yamabe flow without assuming that the boundary is umbilic. Our method is based on estimates for suitable curvature integrals and test functions as well as concentration compactness results.
 
AdviserRugang Ye
SchoolUNIVERSITY OF CALIFORNIA, SANTA BARBARA
SourceDAI/B 69-09, p. , Dec 2008
Source TypeDissertation
SubjectsMathematics
Publication Number3330422
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