17 citations · 44 across the 21 of their papers we have counts for
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The Higher-Dimensional Nitsche Conjecture: Sharp Bounds and Rigidity
Bin Deng, Jiahuan Li, Yilu Liu +1
Let and let $h:\A(r,1)\to\A(R,1)\subset\mathbb R^n$ be an onto homeomorphism with harmonic coordinate functions. We prove the sharp Nitsche bound \[ R\le R_{n,+}(r):=\frac{…
Global Minimality and Rigidity of the Constraint Map Vortex
Bin Deng, Jiahuan Li, Yilu Liu +1
We consider the minimization problem \[ \min\left\{\int_{B_1}|Du|^2:\ u\in W^{1,2}(B_1;\mathbb R^n),\quad u=x\ \text{on }\partial B_1,\quad |u|\ge a\right\}, \quad 0<a<1. \] Figall…
A Brunn--Minkowski inequality and Convexity for the 2-Hessian eigenvalue in convex domains
Jiahuan Li, Xi-Nan Ma, Guohuan Qiu +1
We prove the strict log-concavity of the positive first eigenfunction \(-u\) of the \(2\)-Hessian equation and the strict -convexity of the solution for the corresponding tors…
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…
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…