Lili Wang

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math.SP2026

Weinstock Inequality on Regular Trees

Lili Wang, Tao Wang

Let $T_{n}$ be the infinite $n$ -regular tree, $n \geq 3$ . We prove that every finite connected vertex set $Ω \subset T_{n}$ satisfies the sharp inequality \[ σ_1(Ω)\le \frac{n}{(n-1)|Ω|+1}…

math.SP2026

Counterexamples to Escobar's conjecture

Jin Sun, Lili Wang, Tao Wang

Escobar (J Funct Anal 165(1):101-116, 1999) conjectured that for every $n \geq 3$ , an $n$ -dimensional compact Riemannian manifold with nonnegative Ricci curvature and all boundary pr…

math.SP2026

The Weinstock inequality for convex domains in hyperbolic space

Jin Sun, Lili Wang, Tao Wang

We prove the Weinstock inequality for the first Steklov eigenvalue of convex domains in hyperbolic space $H^{n}$ , resolving Open Question 4.27 of Colbois-Girouard-Gordon-S…