5 papers
Fefferman-SzegÅ kernels and finite-type rigidity on egg domains
Venkata Siddharth Pendyala
We compute the Fefferman boundary measure and the associated Fefferman--SzegÅ kernel for the egg domains $$ E_{n,m}=\{(z,w)\in\mathbb{C}^{n-1}\times\mathbb{C}:\ |z|^2+|w|^{2m}<1\}…
A Degree-Four Lemniscate Path Theorem
Venkata Siddharth Pendyala
We prove the degree-four case of a path problem of ErdÅs, Herzog, and Piranian. If is monic of degree four and all zeros of , counted with multiplicity, lie in the open uni…
Shortest paths in polynomial lemniscate sublevel sets and a problem of ErdÅs
Venkata Siddharth Pendyala
Let be monic, with all zeros in the closed unit disk, and put . Let be the largest possible s…
The Fefferman-SzegÅ Sphericity Criterion in Complex Dimension Three
Venkata Siddharth Pendyala
We establish a Fefferman-SzegÅ characterization of local CR sphericity for smoothly bounded strongly pseudoconvex domains in complex dimension three. We derive the boundary expans…
Sharp order in ErdÅs's minimum-area problem for polynomial lemniscates
Venkata Siddharth Pendyala
For a monic polynomial , its filled unit lemniscate is the planar set . Let denote the least possible area of this set among monic polynomials of degr…