##### Department of Mathematics,

University of California San Diego

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### Math 258 - Differential Geometry

## Takumi Yokota

#### Kyoto University

## Convex functions and barycenters on CAT(1)-spaces of small radii.

##### Abstract:

We establish a new local convex property of CAT(1)-spaces, which are metric spaces of curvature at most 1 in the sense of Aleaxandrov, by showing that a function which has its origin in the study of harmonic maps is convex on any small ball of a CAT(1)-space. As an application, we also discuss barycenters of probability measures on CAT(1)-spaces.

Host: Lei Ni

### February 28, 2013

### 9:00 AM

### AP&M 7218

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