Remarks on quasilocal mass and fill-ins

Abstract

In this paper we would have a brief overview of several proposals of quasilocal mass which are based on Hamiltonian formulation. We also show the positivity of the Wang-Yau energy under a more general condition. We then further study the quasilocal mass and DEC fill-ins defined by the author in terms of completeness and shields.

arXiv comment17 pages, comments are welcome. arXiv admin note: text overlap with arXiv:2109.11070