Bounded Morse index solutions of the Allen-Cahn equation on surfaces

发布时间：2022-06-17 作者：浏览次数：

Speaker:	刘勇	DateTime:	2022年6月22日（周三）下午2:00-3:00
Brief Introduction to Speaker: 刘勇，中国科学技术大学数学学院，特任研究员。2007年获北京大学博士学位，2008.9-2009.9在智利大学数学中心从事博士后研究。主要从事椭圆型偏微分方程的研究工作。今年来主要研究Allen-Cahn、Ginzburg-Landau、KP等方程及与它们相关的可积系统。在J. Reine Angew. Math.、. Arch. Ration. Mech. Anal.、Analysis & PDE Comm. Partial Differential Equations、 Adv. Math. 、 J. Math. Pures Appl.、Ann. Inst. H. Poincaré C Anal. Non Linéaire、 J. Funct. Anal. 、 Int. Math. Res. Not. IMRN 、 Rev. Mat. Iberoam.、 *SIAM J. Math. Anal.* Calc. Var. Partial Differential Equations 等国际知名期刊发表多篇学术论文。		Place:	腾讯会议：582690117
Abstract:Solutions of the Allen-Cahn equation with uniformly bounded Morse index play an important role in the study of p-width of Riemannian manifolds. We are interested in the construction of these type of solutions with multiple transition layers on two dimensional Riemannian manifolds, using Lyapunov-Schmidt reduction. It turns out that these solutions are closely related to the bouncing Jacobi fields of the associated geodesics. We also compute the Morse index of these solutions. In the multiplicity two case, we show that nodal sets of solutions with uniformly bounded Morse index converge, after normalization, to bouncing Jacobi fields.

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