Communications in Analysis and Geometry

Volume 29 (2021)

Number 8

Proof of a null Penrose conjecture using a new quasi-local mass

Pages: 1847 – 1915



Henri P. Roesch (Department of Mathematics, Columbia University, New York, N.Y., U.S.A.)


We define an explicit quasi-local mass functional which is nondecreasing along all doubly convex foliations of null cones. Assuming the existence of a doubly convex foliation, we use this new functional to prove the Null Penrose Conjecture.

The author would like to deeply thank Hubert L. Bray for his supervision and support during the development of these ideas as well as Marc Mars for insightful conversation and his invaluable comments upon a close reading of this paper. The author is also very appreciative for the financial support for his last year of graduate school and for travel to conferences provided by NSF grant DMS-1406396.

Received 26 November 2018

Accepted 23 May 2019

Published 24 May 2022