Geometric Analysis Seminar: Xinran Yu (Illinois)

Title: Boundary Expansions and Singular Yamabe Compactifications in Lovelock Geometry

Abstract: Lovelock geometry extends the Einstein framework to higher-curvature models; it connects naturally to the AdS/CFT correspondence while being sensitive to the dimension. In this talk, I will describe two types of boundary expansions and their applications. The first concerns the metric itself: conformally compact Lovelock metrics admit Fefferman–Graham expansions and carry obstruction tensors generalizing those in the Einstein case. This expansion connects to filling problems where index theory provides topological obstructions. The second concerns the conformal factor in the singular Yamabe–(2q) problem, where one seeks compactifications with constant scalar-(2q) curvature.