Geometry & Geometric Analysis Seminar
The Geometry and Geometric Analysis (GAGA) Seminar is an opportunity for geometers, topologists, and others from TCU and other campuses to learn about new topics of mutual interest. GAGA meets most weeks during the school year. You can find notes from past talks at the GAGA Note Repository, located in a secure off-campus location.
The next meeting of GAGA will be Thursday, November 21 from 4 to 5 pm in Tucker Technology Center (TUC) 243. Sri Rama Chandra Kushtagi from the University of Texas at Dallas will continue speaking on "Volume Renormalization for Singular Yamabe Metrics in Higher Codimension."
Abstract: For a closed embedded submanifold Σn of a closed Riemannian manifold (Mn+k, g), we define extrinsic global conformal invariants of Σn by renormalizing the volume associated to the unique singular Yamabe metric with
singular set Σ. For odd n, the renormalized volume is an absolute conformal invariant,
while for even n, there is a conformally invariant energy term given by the integral
of a local Riemannian invariant. We also compute the derivatives of these quantities
with respect to variations of the submanifold. We compare these results with their
counterparts in the CCE (conformally compact Einstein) and classical singular Yamabe
contexts.
For even-dimensional submanifolds, the notion of energy extends to most codimensions
without the dimensionality constraint when viewed from a formal standpoint, allowing
for an introduction of a larger class of conformal invariants. Even in the exceptional
codimensions, interesting behaviors arise.
This talk is based on my doctoral work under the supervision of Stephen McKeown.