Author

Yi-Lu Liu

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Preprint Sep 2026

Isolated singularities of the capillary equation with negative gravity

We classify isolated singularities of classical solutions to the capillary equation with negative gravity, \[ \operatorname{div}\frac{Du}{\sqrt{1+|Du|^2}}=-u \qquad\text{in }B_R\setminus\{0\}\subset\mathbb R^n, \qquad n\ge2, \] without a priori assumptions on symmetry, sign, one-sided boundedness, or blow-up rate. Ever...

Bing Deng, Jia-Huan Li, Yi-Lu Liu et al. · 0 citations

Preprint Aug 2026

A Local Lewy Theorem for $p$-Harmonic Function with Non-zero Gradient in $R^3$

We establish a local Lewy-type theorem for $p$-harmonic function with non-zero gradient in dimension three space $R^3$. Let $1<p<\infty$, and let $u\in W^{1,p}_{\mathrm{loc}}(\Omega)$ be a weak $p$-harmonic function in a domain $\Omega\subset\mathbb R^3$, assume it satisfies $|Du|>0$, we prove that a locall...

Jia-Huan Li, Yi-Lu Liu, Xi-Nan Ma · 2 citations · ⚡1

Preprint Aug 2026

The Higher-Dimensional Nitsche Conjecture: Sharp Bounds and Rigidity

Let $n\ge3$ 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 \[ R\le R_{n,+}(r):=\frac{nr}{n-1+r^n}, \] and, when $h$ interchanges the two ends, the strictly stronger sharp bound \[ R\le R_{n,-}(r):=\frac{nr^{n-1}}{1+(n-1)r^n}....

Bing Deng, Jia-Huan Li, Yi-Lu Liu et al. · 0 citations