In this talk, I will present recent results on axially symmetric solutions of Allen-Cahn equation. For the existence results, we show in three dimensional Euclidean space the existence of a complete family of axially symmetric solutions with a range of logarithmic growth rates, which may be regarded as the analogue of the family of catenoids and hence called two-end solutions. Nonexistence of two-end solution with a small growth rate is also shown, which differs from the theory of minimal surfaces. For the classification of axially symmetric solutions with finite morse index, we show in dimension three that such solutions have finitely many ends. Furthermore, the solution has exactly two ends if its Morse index equals 1. It is also shown that there does not exist such a solution in dimensions between 4 and 10.
1月9日
11:00am - 12:00pm
地點
Room 3472, Academic Building (Lifts 25-26)
講者/表演者
Prof. Changfeng Gui
University of Texas at San Antonio
主辦單位
Department of Mathematics
聯絡方法
mathseminar@ust.hk
付款詳情
對象
Alumni, Faculty and Staff, PG Students, UG Students
語言
英語
其他活動
3月24日
研討會, 演講, 講座
IAS / School of Science Joint Lecture - Pushing the Limit of Nonlinear Vibrational Spectroscopy for Molecular Surfaces/Interfaces Studies
Abstract Surfaces and interfaces are ubiquitous in Nature. Sum-frequency generation vibrational spectroscopy (SFG-VS) is a powerful surface/interface selective and sub-monolayer sensitive spect...
11月22日
研討會, 演講, 講座
IAS / School of Science Joint Lecture - Leveraging Protein Dynamics Memory with Machine Learning to Advance Drug Design: From Antibiotics to Targeted Protein Degradation
Abstract Protein dynamics are fundamental to protein function and encode complex biomolecular mechanisms. Although Markov state models have made it possible to capture long-timescale protein co...