INTERFACE FOLIATION NEAR MINIMAL SUBMANIFOLDS IN RIEMANNIAN MANIFOLDS WITH POSITIVE RICCI CURVATURE
Publication in refereed journal


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替代計量分析
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其它資訊
摘要Let ( 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|).
著者del Pino M, Kowalczyk M, Wei JC, Yang J
期刊名稱Geometric And Functional Analysis
出版年份2010
月份10
日期1
卷號20
期次4
出版社Springer Verlag (Germany)
頁次918 - 957
國際標準期刊號1016-443X
電子國際標準期刊號1420-8970
語言英式英語
關鍵詞Concentration phenomena; multiple transition layers; positive Gauss curvature
Web of Science 學科類別Mathematics; MATHEMATICS

上次更新時間 2020-18-11 於 23:36