## University of Tennessee - Geometric analysis seminar

### Spring 2020

Thursday, January 9, 17:00, A111

Liming Sun (Johns Hopkins)

Title: Some convexity theorems for translating solitons in the mean curvature flow.

Abstract: I will be talking about the translating solitons (translators) in the mean curvature flow. Convexity theorems for translators play fundamental roles in the classification of them. Spruck and Xiao proved any two dimensional mean convex translator is actually convex. We proved a similar convexity theorem for higher dimensional translators, namely the 2-convex translating solitons are actually convex. Our theorem implies that 2-convex translating solitons have to be the bowl soliton. Our second theorem regards the solutions of the Dirichlet problem for translators in a bounded convex domain. We proved the solutions will be convex under appropriate conditions. This theorem implies the existence of an (*n–2*)-parameter family of locally strictly convex translators in higher dimensions. In the end, we will show that our method could be used to establish a convexity theorem for constant mean curvature graph equation.

Thursday, February 27, 17:00, A111

Alina Stancu (Concordia)

Title: On a curvature flow and some of its applications

Abstract: We study a version of Ben Andrews’ curvature flow on convex hypersurfaces in *R*^{n} whose pointwise speed in the direction of the affine normal is determined by a time-independent weight with nice properties. We show that for each smooth, strictly convex initial hypersurface the flow exists until it develops a point singularity and the, properly rescaled, solutions to the flow converge smoothly to a certain class of hypersurfaces. We will discuss some applications of this convergence to geometric inequalities.

(**Departmental Colloquium**) Friday, February 28, 15:35, A405

Frank Morgan (Williams College)

Title: Isoperimetric Problems

Abstract: The Ancient Greeks proved that the circle is the least-perimeter way to enclose given area in the plane. What about other spaces? Such isoperimetric questions are now playing as large a role as ever throughout mathematics and applications. We'll discuss some open questions and recent results, some by undergraduates.

(*Frank will also deliver a jr. colloquium on Thursday, February 27 at 15:35 in A405*)

Thursday, March 12, 17:00, A111

Alex Mramor (Johns Hopkins)

Title: Some recent results on rotationally symmetric self shrinkers to the mean curvature flow.

Abstract: In this talk I’ll discuss some recent compactness and finiteness results for rotationally symmetric self shrinkers.

**CANCELLED due to CoViD-19 outbreak**

(**Analysis Seminar**) Wednesday, April 1, 14:30, A112

Silvia Ghinassi (IAS)

Title: TBA

Abstract: TBA

**CANCELLED due to CoViD-19 outbreak**

Thursday, April 16, 17:00, A111

Alec Payne (NYU)

Title: TBA

Abstract: TBA

**CANCELLED due to CoViD-19 outbreak**

Thursday, April 23, 17:00, A111

Stefano Nardulli (Princeton and Universidade Federal do ABC )

Title: TBA

Abstract: TBA

**CANCELLED due to CoViD-19 outbreak**

Thursday, April 30, 17:00, A111

Huy The Nguyen (Queen Mary University of London)

Title: TBA

Abstract: TBA

**CANCELLED due to CoViD-19 outbreak**

Back to seminar page.