From the 1 of 7 linked papers with an AI index.
7 papers
Strict Concavity of the Torsion Function for the Restricted Half-Laplacian in Bounded Convex Domains
Jiahuan Li, Shujun Shi
Let , , be a bounded convex domain, and let be the torsion function for the restricted half-Laplacian. We prove that is negative definit…
A Local Lewy Theorem for -Harmonic Function with Non-zero Gradient in
Jiahuan Li, Yilu Liu, Xi-Nan Ma
We establish a local Lewy-type theorem for \(p\)-harmonic function with non-zero gradient in dimension three space . Let \(1<p<\infty\), and let \(u\in W^{1,p}_{\mathrm{loc}}(…
Nonconvex Sublevel Sets For The Planar Translating Mean Curvature Equation
Jiahuan Li, Yilu Liu, Xi-Nan Ma +1
Translating solitons arise as models for type~II singularities of mean-convex mean curvature flow. We construct a smooth bounded uniformly convex domain \(\Om\Subset\R^2\) such tha…
Strict Convexity for Solution of Liouville-Type Dirichlet Problems
Jiahuan Li, Shuning Xu
The paper proves that a transformed solution of three exponential Dirichlet problems on smooth uniformly strictly convex domains is strictly convex, using techniques like domain de…
Bernstein-type theorem for stationary hypersurfaces of the Euler-Dierkes-Huisken functional
Hongbin Cui, Jiahuan Li, Xiaowei Xu
We say that a hypersurface is -stationary if it is a critical point of the Euler-Dierkes-Huisken functional $\mathcal{E}_α(Σ)=\int_Σ|X|^α\, d\ma…
Brunn--Minkowski Inequality for the First Complex -Hessian Eigenvalue
Chuanqiang Chen, Jiahuan Li, Xi-Nan Ma
There are relatively few results on the convexity of solutions to complex equations. In this paper, We prove a strict real log-concavity theorem for the first eigenfunction of the…