6 papers · 1 filter
Bounds of Scalar curvature, S-curvature and distortion on -Einstein Finsler manifolds
Bin Shen
This manuscript investigates the curvature and topological properties of certain -Einstein Finsler metrics on Finsler metric measure spaces. By imposing symmetry conditions…
Gradient estimates and Harnack inequality for positive solutions to the heat equation under compact Finsler geometric flows
Bin Shen
In this manuscript, we extend the global gradient estimates for positive solutions to the heat equation under a general compact Finsler geometric flow and derive the cor…
A Liouville-type theorem for Finslerian exponentially harmonic functions
Bin Shen
In this manuscript, we investigate the exponentially harmonic equation on noncompact forward complete Finsler metric measure spaces. We demonstrate that this Finslerian equation re…
Li-Yau Estimates for a Nonlinear Parabolic Equation on Finsler Manifolds
Bin Shen, Yuhan Zhu
In this paper, we explore the positive solutions to the Finslerian nonlinear equation which is related to Ricci…
Gradient estimates of the Finslerian Allen-Cahn equation
Bin Shen
In this manuscript, we study bounded positive solutions to the Finslerian Allen-Cahn equation. The Allen-Cahn equation is widely applied and connected to many mathematical branches…
Operators on nonlinear metric measure spaces I: A New Laplacian comparison theorem on Finsler manifolds and a generalized Li-Yau approach to gradient estimates of Finslerian Schrödinger equation
Bin Shen
This paper is the first in a series of paper where we describe the differential operators on general nonlinear metric measure spaces, namely, the Finsler spaces. We try to propose…