3 papers
math.AP2026
Relative isoperimetry in the three-dimensional cube: classification and quantitative stability
Bin Deng, Jiahuan Li, Yilu Liu
We determine the complete relative isoperimetric profile of the three-dimensional unit cube and classify all minimizing sets, including the equality cases at both transition volume…
math.AP2026
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{…
math.AP2026
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…