Pengfei Guan

activity

20022025

most citedA Microscopic Convexity Principle for Nonlinear Partial Differential Equations

107 citations · 368 across the 25 of their papers we have counts for

collaborators

25 papers

math.DG2025

Intrinsicality of second fundamentals of hypersurfaces in space form

Pengfei Guan, Yu Yuan

We prove that the normalized second fundamental form $A$ of immersed $C^{2}$ hypersurface in a space form $(N^{n + 1}, g ˉ)$ is intrinsic provided $σ_{2 k + 1} (A) \neq = 0$ for some $k\ge…

math.AP2023

Anisotropic flow, entropy and $L^{p}$ -Minkowski problem

Károly J. Böröczky, Pengfei Guan

We provide a natural simple argument using anistropic flows to prove the existence of weak solutions to Lutwak's $L^{p}$ -Minkowski problem on $S^{n}$ which were obtained by other metho…

math.AP2021★ 32 cited

A fully-nonlinear flow and quermassintegral inequalities in the sphere

Chuanqiang Chen, Pengfei Guan, Junfang Li +1

This expository paper presents the current knowledge of particular fully nonlinear curvature flows with local forcing term, so-called locally constrained curvature flows. We focus…

math.AP2019★ 16 cited

A class of curvature type equations

Pengfei Guan, Xiangwen Zhang

In this paper, we study the solvability of a general class of fully nonlinear curvature equations, which can be viewed as generalizations of the equations for Christoffel-Minkowski…

math.DG2017★ 45 cited

Interior C2 regularity of convex solutions to prescribing scalar curvature equations

Pengfei Guan, Guohuan Qiu

We establish interior $C^{2}$ estimates for convex solutions of scalar curvature equation and $σ_{2}$ -Hessian equation. We also prove interior curvature estimate for isometrically imme…

math.DG2017

$L^{p}$ Christoffel-Minkowski problem: the case $1 < p < k + 1$

Pengfei Guan, Chao Xia

We consider a fully nonlinear partial differential equation associated to the intermediate $L^{p}$ Christoffel-Minkowski problem in the case $1 < p < k + 1$ . We establish the existence of…