# Analysis Seminar

#### Symmetry, Quantitative Liouville Theorems and Analysis of Large Solutions of Conformally Invariant Fully Nonlinear Elliptic Equations

**Speaker:**
Yanyan Li, Rutgers University

**Location:**
Warren Weaver Hall 1302

**Date:**
Thursday, April 28, 2016, 11 a.m.

**Synopsis:**

We establish blow-up profiles for any blowing-up sequence of solutions of general conformally invariant fully nonlinear elliptic equations on Euclidean domains. We prove that (i) the distance between blow-up points is bounded from below by a universal positive number, (ii) the solutions are very close to a single standard bubble in a universal positive distance around each blow-up point, and (iii) the heights of these bubbles are comparable by a universal factor. As an application of this result, we establish a quantitative Liouville theorem. This is a joint work with Luc Nguyen.