Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	姚若飞,华南理工大学
Inviter:	彭发
Title:	Uniqueness of critical points of the second Neumann eigenfunctions on triangles
Language:	Chinese
Time & Venue:	2023.09.20 15:00-16:00 腾讯会议：171-452-410
Abstract:	The celebrated hot spots conjecture says that the second Neumann eigenfunctions attain their global maximum (hottest point) only on the boundary of the domain. When the domain is a triangle, the nonexistence of interior critical point was proved in a recent paper by Judge and Mondal [Ann. Math., 2022], however, several open problems regarding the second Neumann eigenfunction in triangles remained open. In our talk, we answer these unresolved problems, including (1) the uniqueness of non-vertex critical point, (2) the sufficient and necessary conditions for the existence of non-vertex critical point, (3) the exact location of the global extrema. (4) the location of endpoints of the nodal line, and so on. Our approach employs the continuity methods via domain deformation. This is a joint work with Prof. Hongbin Chen and Prof. Changfeng Gui.