中国科大学位与研究生教育
课程名称: 教师:
当前位置:
 >> 
 >> 
Interface foliation near minimal submanifolds in Riemannian manifolds with Positive Ricci curvature
Interface foliation near minimal submanifolds in Riemannian manifolds with Positive Ricci curvature
教师介绍

本讲教师:杨 军
所属学科:理科
人  气:614

课程介绍
Abstract:We will talk about the construction of clustering interfaces for Allen-Cahn equation on compact Riemannian manifold by the infinitely dimensional reduction method(from "M. del Pino, M. Kowalczyk, J. Wei, Comm. Pure Appl. Math. 2007"). The interaction of neighbouring interfaces will be derived in a form of Toda-Jacobi System involving a resonance phenomena. The result appeared in "M. del Pino, M. Kowalczyk, J. Wei and J. Yang, Interface foliation near minimal submanifolds in Riemannian manifolds with positive Ricci curvature, Geometric and Functional Analysis, 20 (2010), no. 4, 918-957". Let $(M , K)$ be an $N$-dimensional smooth compact Riemannian manifold. We consider the singularly perturbed Allen-Cahn equation $$epsilon^2Delta_g u,+, (1 - u^2)u ,=,0quad mbox{in } M,$$ where $epsilon$ is a small parameter. Let $Ksubset M$ be an $(N-1)$-dimensional smooth minimal submanifold that separates $M$ into two disjoint components. Assume that $K$ is non-degenerate in the sense that it does not support non-trivial Jacobi fields, and that $|A_K|^2+mbox{Ric}_g(nu_K, nu_K)$ is positive along $K$. Then for each integer $mgeq 2$, we establish the existence of a sequence $epsilon = epsilon_jto 0$, and solutions $u_epsilon$ with $m$-transition layers near $K$, with mutual distance $O(epsilon|ln epsilon|)$.

评论

针对该课程没有任何评论,谈谈您对该课程的看法吧?
  • 用户名: 密 码:
致谢:本课件的制作和发布均为公益目的,免费提供给公众学习和研究。对于本课件制作传播过程中可能涉及的作品或作品部分内容的著作权人以及相关权利人谨致谢意!
课件总访问人次:17031421
中国科学技术大学研究生网络课堂试运行版,版权属于中国科学技术大学研究生院。
本网站所有内容属于中国科学技术大学,未经允许不得下载传播。
地址:安徽省合肥市金寨路96号;邮编:230026。TEL:+86-551-63602922;E-mail:wlkt@ustc.edu.cn。