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Pingxin Gu

Publications and source records attributed to Pingxin Gu.

4 recordsLinked to original sources
arXiv2026

Isodiametric-type upper bounds for Steklov eigenvalues

In this paper, we establish isodiametric-type upper bounds for Steklov eigenvalues of bounded Lipschitz domains $\Omega\subset \mathbb{R}^n$, $n\geq 2$, valid for every $k\in \mathbb{N}$: \[ D(\Omega)\sigma_k(\Omega)\leq C(n)k, \] \[ D(\Omega)\sigma_k(\Omega)\leq C(n)k^2\left(\frac{|\Omega|^{\frac{1}{n}}}{D(\Omega)}\right)^{\frac{n}{n-1}}, \] where $C(n)>0$ depends only on $n$. The first estimate is sharp in its linear dependence on $k$, while the second is sharp both in the exponent of the volume-diameter ratio and, once that exponent is fixed, in its quadratic dependence on $k$. In particular, the second estimate gives an affirmative answer to Open Question 4.37 in [5].

math.DG↗
arXiv2026

Weinstock inequality in hyperbolic space II

In this paper, we establish the Weinstock inequality for the first non-zero Steklov eigenvalue on star-shaped mean convex domains in hyperbolic space $\mathbb{H}^n$ for $n\geq 3$. We note that when $n\geq 4$, the result was obtained in our previous paper [23]. In particular, when the domain is convex, our result gives an affirmative answer to Open Question 4.27 in [13] for the hyperbolic case.

math.DG↗
arXiv2024

Weinstock inequality in hyperbolic space

In this paper, we establish the Weinstock inequality for the first non-zero Steklov eigenvalue on star-shaped mean convex domains in hyperbolic space $\mathbb{H}^n$ for $n \geq 4$. In particular, when the domain is convex, our result gives an affirmative answer to Open Question 4.27 in [7] for the hyperbolic space $\mathbb{H}^n$ when $n \geq 4$.

math.DG↗