11-27【Zhixin Wang】Neumann Data and Second Variation Formula of Renormalized Area for Conformally Compact Static Spaces

Time:2025-11-04Views:10

Speaker: Zhixin Wang (Shanghai Jiao Tong University)

Time: 14:30-15:30, Nov 27, 2025

Venue: room 1329, Building 1 (Section A), New Campus, Shanghai Institute for Advanced Studies, USTC & Tencent Meeting ID: 942 663 0176, password: 202501


     

In this paper, we derive the first and second variation formulas for the renormalized area for static Einstein spaces along a specific direction for $n=3$, demonstrating that the negativity of the Neumann data implies instability. Consequently, we obtain a rigidity result for the case when the conformal boundary is a warped product torus, which strengthens a previous result. The rigidity result can be generalized to $n\leq 7$.


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