授课人：姚若飞（华南理工大学）

时间：3月4日 19:00-21:30, 3月5日19:00-21:30，3月6日14:00-16:00

地点：数学学院（新楼）308会议室

题目：Hot Spots Conjecture on triangles

摘要:  The Hot Spots Conjecture is a classical problem in spectral geometry and partial differential equations, with a history of more than fifty years, originating in the work of Rauch in the 1970s. It predicts that the second Neumann eigenfunction of the Laplacian attains its global maximum (the “hottest spot”) exclusively on the boundary of the domain. While the conjecture remains open for general planar convex domains, it has been proved for certain special classes of domains, including symmetric and sufficiently narrow ones, in which the arguments are already highly nontrivial. In this talk, we report some recent progress on the Hot Spots Conjecture for triangular domains.

1. Historical Background of the Hot Spots Conjecture and the Continuity Method. 

2. Monotonicity and Uniqueness of Critical Points. 

3. Geometric Location of Level Sets.