**Medians and Means in Riemannian Geometry: Existence, Uniqueness and Computation**

by M. Arnaudon, F. Barbaresco, L. Yang

**Publisher**: arXiv 2011**Number of pages**: 48

**Description**:

This paper is a short summary of our recent work on the medians and means of probability measures in Riemannian manifolds. Firstly, the existence and uniqueness results of local medians are given. In order to compute medians in practical cases, we propose a subgradient algorithm and prove its convergence.

Download or read it online for free here:

**Download link**

(900KB, PDF)

## Similar books

**Semi-Riemann Geometry and General Relativity**

by

**Shlomo Sternberg**

Course notes for an introduction to Riemannian geometry and its principal physical application, Einsteinâ€™s theory of general relativity. The background assumed is a good grounding in linear algebra and in advanced calculus.

(

**13031**views)

**Lectures on Geodesics in Riemannian Geometry**

by

**M. Berger**-

**Tata Institute of Fundamental Research**

The main topic of these notes is geodesics. Our aim is to give a fairly complete treatment of the foundations of Riemannian geometry and to give global results for Riemannian manifolds which are subject to geometric conditions of various types.

(

**5068**views)

**An Introduction to Riemannian Geometry**

by

**Sigmundur Gudmundsson**-

**Lund University**

The main purpose of these lecture notes is to introduce the beautiful theory of Riemannian Geometry. Of special interest are the classical Lie groups allowing concrete calculations of many of the abstract notions on the menu.

(

**9664**views)

**Riemannian Geometry**

by

**Ilkka Holopainen, Tuomas Sahlsten**

Based on the lecture notes on differential geometry. From the contents: Differentiable manifolds, a brief review; Riemannian metrics; Connections; Geodesics; Curvature; Jacobi fields; Curvature and topology; Comparison geometry; The sphere theorem.

(

**3890**views)