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# Mathematical Research Letters

## Volume 27 (2020)

### Number 3

### On Hawking mass and Bartnik mass of CMC surfaces

Pages: 855 – 885

DOI: https://dx.doi.org/10.4310/MRL.2020.v27.n3.a12

#### Authors

#### Abstract

Given a constant mean curvature surface that bounds a compact manifold with nonnegative scalar curvature, we obtain intrinsic conditions on the surface that guarantee the positivity of its Hawking mass. We also obtain estimates of the Bartnik mass of such surfaces, without assumptions on the integral of the squared mean curvature. If the ambient manifold has negative scalar curvature, our method also applies and yields estimates on the hyperbolic Bartnik mass of these surfaces.

The work of PM was partially supported by Simons Foundation Collaboration Grant for Mathematicians #585168.

The work of YW was partially supported by National Natural Science Foundation of China #11401168, #11671089.

The work of NX was partially supported by National Natural Science Foundation of China #11671089.

Received 25 September 2018

Accepted 18 February 2019

Published 20 August 2020