We study the existence of positive functions K in C^1(S^n) such that the conformal Q-curvature equation Pm(v) = K v^{n*} on S^n has a singular positive solution v whose singular set is a single point, where m is an integer satisfying 1 <= m < n/2 and Pm is the intertwining operator of order 2m. More specifically, we show that when n => 2 m + 4, every positive function in C^1(S^n) can be approximated in the C^1(S^n) norm by a positive function K in C^1(S^n) such that the equation has a singular positive solution whose singular set is a single point. Moreover, such a solution can be constructed to be arbitrarily large near its singularity.
4月21日
10:00am - 11:00am

地點
https://hkust.zoom.us/j/97977020004 (Passcode:188)
講者/表演者
Mr. Xusheng DU
主辦單位
Department of Mathematics
聯絡方法
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...