V. Pendyala

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math.CV2026

Fefferman-Szegő kernels and finite-type rigidity on egg domains

Venkata Siddharth Pendyala

We compute the Fefferman boundary measure and the associated Fefferman--Szegő kernel for the egg domains $$ E_{n,m}=\{(z,w)\in\mathbb{C}^{n-1}\times\mathbb{C}:\ |z|^2+|w|^{2m}<1\}.…

math.CV2026

A Degree-Four Lemniscate Path Theorem

Venkata Siddharth Pendyala

We prove the degree-four case of a path problem of Erdős, Herzog, and Piranian. If $f$ is monic of degree four and all zeros of $f$ , counted with multiplicity, lie in the open unit…

math.CV2026

Shortest paths in polynomial lemniscate sublevel sets and a problem of Erdős

Venkata Siddharth Pendyala

Let $f (z) = \prod_{j = 1}^{n} (z - a_{j})$ be monic, with all zeros in the closed unit disk, and put $E_{f} = {z \in C : ∣ z ∣ \leq 1, ∣ f (z) ∣ \leq 1}$ . Let $S (n)$ be the largest possible s…

math.CV2026

The Fefferman-Szegő Sphericity Criterion in Complex Dimension Three

Venkata Siddharth Pendyala

We establish a Fefferman-Szegő characterization of local CR sphericity for smoothly bounded strongly pseudoconvex domains in complex dimension three. We derive the boundary expansi…

math.CV2026

Sharp order in Erdős's minimum-area problem for polynomial lemniscates

Venkata Siddharth Pendyala

For a monic polynomial $p$ , its filled unit lemniscate is the planar set $z : ∣ p (z) ∣ < 1$ . Let $κ_{n} (K, 1)$ denote the least possible area of this set among monic polynomials of degre…