I will talk a proof of the conjecture of Alexander and Currier on the embeddedness of a nonnegatively curved hypersurfaces in hyperbolic space. I will also discuss some recent works on hypersurfaces with nonnegative Ricci curvature in hyperbolic space.

# Differential Geometry & Geometric Analysis Seminar

The Differential Geometry and Geometry Analysis seminar sees talks most often about interactions between elliptic PDE's and differential geometry. Common topics include (but are not limited to) conformal geometry, minimal surfaces and other variational problems, K\"ahler geometry, CR geometry, elliptic problems from general relativity, nonlinear and/or nonlocal elliptic or parabolic PDE's, and geometric functional inequalities.

For more information about this seminar, contact Otis Chodosh or Daniel Ketover.

**Please click on seminar title for complete abstract.**

##### Embeddedness and convexity for hypersurfaces in hyperbolic space

UC Santa Cruz

##### TBA - Costante Bellettini

UCLA

##### TBA - Xin Zhou

UC Santa Barbara

##### Multiplicity of constant Q-curvature metrics

I will describe some multiplicity result about constant Q-curvature metrics in the case of homogeneous vibrations and in the case of non compact manifolds related to a singular version of the Q-curvature problem.

Johns Hopkins University

##### TBA - Yannick Sire

Johns Hopkins University

##### TBA - Jeremy Tyson

University of Illinois at Urbana-Champaign

##### TBA - Marco Guaraco

University of Chicago