7 citations · 9 across the 8 of their papers we have counts for
13 papers
On the dimension of bundle-valued Bergman spaces on compact Riemann surfaces
Anne-Katrin Gallagher, Purvi Gupta, Liz Vivas
Given a holomorphic vector bundle over a compact Riemann surface , and an open set in , we prove that the Bergman space of holomorphic sections of the restriction of…
Volume Approximation of Strongly -Convex Domains by Random Polyhedra
Siva Athreya, Purvi Gupta, D. Yogeshwaran
Polyhedral-type approximations of convex-like domains in have been considered recently by the second author. In particular, the decay rate of the error in optimal vo…
Constructing Group-Invariant CR Mappings
Jennifer Brooks, Sean Curry, Dusty Grundmeier +4
We construct CR mappings between spheres that are invariant under actions of finite unitary groups. In particular, we combine a tensoring procedure with D'Angelo's construction of…
On the dimension of Bergman spaces on
Anne-Katrin Gallagher, Purvi Gupta, Liz Vivas
Inspired by a result by Szőke, we give potential-theoretic characterizations of the dimension of the Bergman space of holomorphic sections of a restriction of a holomorphic line bu…
Polynomially convex embeddings of odd-dimensional closed manifolds
Purvi Gupta, Rasul Shafikov
It is shown that any smooth closed orientable manifold of dimension , , admits a smooth polynomially convex embedding into . This improves by …
Hardy Spaces for a Class of Singular Domains
Anne-Katrin Gallagher, Purvi Gupta, Loredana Lanzani +1
We set a framework for the study of Hardy spaces inherited by complements of analytic hypersurfaces in domains with a prior Hardy space structure. The inherited structure is a filt…
Stability of the hull(s) of an -sphere in
Purvi Gupta, Chloe Urbanski Wawrzyniak
We study the (global) Bishop problem for small perturbations of --- the unit sphere of --- in . We show that if $S\s…
The Rational Hull of Rudin's Klein Bottle
John T. Anderson, Purvi Gupta, Edgar L. Stout
In this note, a general result for determining the rational hulls of fibered sets in is established. We use this to compute the rational hull of Rudin's Klein bottle…
Polynomially Convex Embeddings of Even-Dimensional Compact Manifolds
Purvi Gupta, Rasul Shafikov
The totally-real embeddability of any -dimensional compact manifold into , , has several consequences: the genericity of polynomially convex embeddin…
A nonpolynomially convex isotropic two-torus with no attached discs
Purvi Gupta
We show --- with the means of a real-analytic example in --- that Gromov's theorem on the presence of attached holomorphic discs for compact Lagrangian manifolds is…
Convex Floating Bodies as Approximations of Bergman Sublevel Sets on Tube Domains
Purvi Gupta
For a pseudoconvex tube domain, we prove estimates that relate the sublevel sets of its diagonal Bergman kernel to the floating bodies of its convex base. This allows us to associa…
Rational and Polynomial Density on Compact Real Manifolds
Purvi Gupta, Rasul Shafikov
We establish a characterization for an -manifold to admit functions ,..., and functions in so that every element…
Volume Approximations of Strictly Pseudoconvex Domains
Purvi Gupta
In convex geometry, the Blaschke surface area measure on the boundary of a convex domain can be interpreted in terms of the complexity of approximating polyhedra. In response to a…