INTERFACE FOLIATION NEAR MINIMAL SUBMANIFOLDS IN RIEMANNIAN MANIFOLDS WITH POSITIVE RICCI CURVATURE
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AbstractLet ( M, (g) over tilde) be an N- dimensional smooth compact Riemannian manifold. We consider the singularly perturbed Allen- Cahn equation epsilon(2)Delta (g) over tildeu + ( 1 - u(2)) u = 0 in M, where e is a small parameter. Let K subset of M be an ( N- 1)-dimensional smooth minimal submanifold that separates M into two disjoint components. Assume that K is nondegenerate in the sense that it does not support non- trivial Jacobi fields, and that |A(K)|(2) + Ric (g) over tilde (nu(K),nu(K)) is positive along K. Then for each integer m >= 2, we establish the existence of a sequence epsilon = epsilon(j) -> 0, and solutions ue with m- transition layers near K, with mutual distance O( epsilon| ln epsilon|).
All Author(s) Listdel Pino M, Kowalczyk M, Wei JC, Yang J
Journal nameGeometric And Functional Analysis
Year2010
Month10
Day1
Volume Number20
Issue Number4
PublisherSpringer Verlag (Germany)
Pages918 - 957
ISSN1016-443X
eISSN1420-8970
LanguagesEnglish-United Kingdom
KeywordsConcentration phenomena; multiple transition layers; positive Gauss curvature
Web of Science Subject CategoriesMathematics; MATHEMATICS

Last updated on 2020-28-10 at 00:18