Pengzi Miao

Professor

Phone:
(305) 284-2859
Locator Code:
4250
 
Career

Education

2003Ph.D. Mathematics Stanford University
1998B.S. Mathematics Peking University

LIST OF SPECIALTIES: Differential Geometry and Mathematical Relativity.

LIST OF SPECIALTIES: Differential Geometry and Mathematical Relativity.

Research

LIST OF SPECIALTIES: Differential Geometry and Mathematical Relativity.

Publications

Siyuan Lu, Pengzi Miao "Variation and rigidity of quasi-local mass" (27 Feb 2018 ). [Link]

SUMMARY: Inspired by the work of Chen-Zhang \cite{Chen-Zhang}, we derive an evolution formula for the Wang-Yau quasi-local energy in reference to a static space, introduced by Chen-Wang-Wang-Yau \cite{CWWY}. If the reference static space represents a mass minimizing, static extension of the initial surface Σ, we observe that the derivative of the Wang-Yau quasi-local energy is equal to the derivative of the Bartnik quasi-local mass at Σ
Combining the evolution formula for the quasi-local energy with a localized Penrose inequality proved in \cite{Lu-Miao}, 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.

C. Li, Z. Wang and P. Miao "Uniqueness of isometric immersions with the same mean curvature" J. Funct. Anal. [Link]


More Publications