##### Department of Mathematics,

University of California San Diego

****************************

### Colloquium Seminar

## Prof. Or Hershkovits

#### Hebrew University of Jerusalem

## Mean curvature flow in spaces with positive cosmological constant

##### Abstract:

In this talk, I will describe an approach of using Lorentzian mean curvature flow (MCF) to probe "expanding universes" (such as, presumably, ours) with matter that is assumed to be attracted to matter (formally, this assumption is called the "strong energy condition")

Assuming 2-dimensional symmetry, I will explain how the mean curvature flow can be used to show that such universes become asymptotic, in some sense, to the maximally symmetric such universe - de Sitter space. This proves a special case of the de Sitter no hair conjecture of Hawking and Gibbons.

Unfortunately, the early universe did not support such two-dimensional symmetry, rendering the above mentioned result physically insignificant. As a first step for removing the above symmetry assumption, I will illustrate a condition, natural in the above context, such that any local graphical mean curvature flow (without symmetry) in de Sitter space satisfying that condition converges to a certain "universal flow".

Effort will be made to make the talk accessible to the wide mathematical audience. In particular, no "physics reasoning" will be involved. This is based on a joint work with Creminelli, Senatore and Vasy, and on a joint work with Senatore.

Host: Spolaor Luca

### January 17, 2024

### 4:15 PM

APM 6402

****************************