Variation and rigidity of quasi-local mass

Siyuan Lu, Pengzi Miao

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Inspired by the work of Chen-Zhang [5], we derive an evolution formula for theWang-Yau quasi-local energy in reference to a static space, introduced by Chen-Wang-Wang-Yau [4]. If the reference static space represents a mass minimizing, static extension of the initial surface ∑, we observe that the derivative of the Wang-Yau quasi-local energy is equal to the derivative of the Bartnik quasilocal mass at ∑. Combining the evolution formula for the quasi-local energy with a localized Penrose inequality proved in [9], we prove a rigidity theorem for compact 3-manifolds with nonnegative scalar curvature, with boundary. This rigidity theorem in turn gives a characterization of the equality case of the localized Penrose inequality in 3-dimension.

Original languageEnglish (US)
Pages (from-to)1411-1426
Number of pages16
JournalAdvances in Theoretical and Mathematical Physics
Issue number5
StatePublished - 2019

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)


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