arXiv subjects

Harshith Alagandala

Publications and source records attributed to Harshith Alagandala.

2 recordsLinked to original sources

arXiv2026

Carleman Approximation for certain sets with an isolated singularity

In this paper, we prove that local polynomial convexity at the origin for the union of finitely many transverse totally real subspaces of maximal dimension is sufficient for Carleman approximation. Some new conditions are given for the polynomial convexity of the union of three transverse totally real planes in $\mathbb{C}^2$. We also provide a sufficient condition on the union of two Lipschitz graphs for Carleman approximation. Along the way, we provide sufficient conditions for union of two Lipschitz graphs to be polynomially convex. Finally, we find a family of surfaces in $\mathbb{C}^2$ with a hyperbolic complex point that allows Carleman approximation.

math.CV↗

arXiv2025

Local Polynomial Convexity at Hyperbolic CR-singularities in $M \subset \mathbb{C}^n$

Let $M$ be a smooth manifold of dimension $n$ embedded in $\mathbb{C}^n$. If $T_pM \subset T_p\mathbb{C}^n$ is a totally real subspace for $p\in M$, then $M$ is locally polynomially convex at $p$. For a generic embedding $M$, we are interested in assessing polynomial convexity of $M$ at a CR-singularity, i.e., at a point $p\in M$ where $T_pM$ is not totally real. An order one CR-singularity in $M$ can be broadly classified as elliptic and hyperbolic. It is known that elliptic points give obstruction to polynomial convexity. In the case $n=2$, $M^2 \subset \mathbb{C}^2$ is locally polynomially convex at a hyperbolic complex point. We investigate local polynomial convexity of $M^n \subset \mathbb{C}^n$ at hyperbolic points in higher dimension.

math.CV↗