72 citations · 441 across the 54 of their papers we have counts for
55 papers
Monotonicity of harmonic functions on -manifolds with an asymptotically flat end
Pengzi Miao
We derive monotone properties of positive harmonic functions on three dimensional manifolds with nonnegative scalar curvature, with an asymptotically flat end. Rigidity characteriz…
Horizons in noncompact fill-ins of nonnegative scalar curvature
Pengzi Miao, Sehong Park
Given a complete Riemannian metric of nonnegative scalar curvature on , where denotes a -sphere, we exhibit conditions that imply the existence of a…
Implications of some mass-capacity inequalities
Pengzi Miao
Applying a family of mass-capacity related inequalities proved in \cite{M22}, we obtain sufficient conditions that imply the nonnegativity as well as positive lower bounds of the m…
Estimates of the Bartnik mass
Pengzi Miao, Annachiara Piubello
Given a metric of nonnegative Gauss curvature and a positive function on a -sphere , we estimate the Bartnik quasi-local mass of in terms of the area, the…
Monotone quantities of -harmonic functions and their applications
Sven Hirsch, Pengzi Miao, Luen-Fai Tam
We derive local and global monotonic quantities associated to -harmonic functions on manifolds with nonnegative scalar curvature. As applications, we obtain inequalities relatin…
Mass, capacitary functions, and the mass-to-capacity ratio
Pengzi Miao
We study connections among the ADM mass, positive harmonic functions tending to zero at infinity, and the capacity of the boundary of asymptotically flat -manifolds with nonnega…