# ProjectBartnik – PPP Australien: Bartniks Massenfunktional -- Cederbaum, McCormick

## Basic data

Acronym:

Bartnik

Title:

PPP Australien: Bartniks Massenfunktional -- Cederbaum, McCormick

Duration:

1/1/2016 to 12/31/2017

Abstract / short description:

This project is in Mathematical General Relativity (GR). In 1989, Robert Bartnik defined a functional assigning a “mass” to a set of “Bartnik data“: a Riemannian metric and a prescribed (positive) mean curvature function H on the 2-sphere. This mass is defined as the infimum of the total (ADM) mass over all asymptotically flat Riemannian manifolds with non-negative scalar curvature into which the given data isometrically embed as outer minimizing inner boundary. Bartnik’s mass is relevant for the theoretical foundations of GR as it satisfies many desirable properties suggested by Christodoulou-Yau.

Understanding whether minimizers exist is crucial for physical applicability of Bartnik’s mass.

Understanding whether minimizers exist is crucial for physical applicability of Bartnik’s mass.

Keywords:

quasi-local mass

calculus of variations

mathematical relativity

minimizing sequences

## Involved staff

### Managers

Department of Mathematics

Faculty of Science

Faculty of Science

## Local organizational units

Department of Mathematics

Faculty of Science

University of Tübingen

University of Tübingen

## Funders

Bonn, Nordrhein-Westfalen, Germany