7 citations · 28 across the 12 of their papers we have counts for
13 papers
CR functions at CR singularities: approximation, extension, and hulls
Jiri Lebl, Alan Noell, Sivaguru Ravisankar
We study three possible definitions of the notion of CR functions at CR singular points, their extension to a fixed-neighborhood of the singular point, and analogues of the Baouend…
The Friedrichs Operator and Circular Domains
Sivaguru Ravisankar, Samriddho Roy
The Friedrichs operator of a domain (in ) is closely related to its Bergman projection and encodes crucial information (geometric, quadrature, potential theoretic etc…
Conformal Rigidity of Polar Set Complements
Ratna Pal, Koushik Ramachandran, Sivaguru Ravisankar
Let be a closed polar subset of . In this short note, we use elementary potential theoretic tools to show that any conformal map on is nece…
Cartan uniqueness theorem on nonopen sets
Jiri Lebl, Alan Noell, Sivaguru Ravisankar
Cartan's uniqueness theorem does not hold in general for CR mappings, but it does hold under certain conditions guaranteeing extendibility of CR functions to a fixed neighborhood.…
On CR singular CR images
Jiří Lebl, Alan Noell, Sivaguru Ravisankar
We say that a CR singular submanifold has a removable CR singularity if the CR structure at the CR points of extends through the singularity as an abstract CR structure on…
A CR singular analogue of Severi's theorem
Jiri Lebl, Alan Noell, Sivaguru Ravisankar
Real-analytic CR functions on real-analytic CR singular submanifolds are not in general restrictions of holomorphic functions, unlike in the CR nonsingular case. We give a simple c…
On the Levi-flat Plateau problem
Jiri Lebl, Alan Noell, Sivaguru Ravisankar
We solve the Levi-flat Plateau problem in the following case. Let , , be a connected compact real-analytic codimension-two submanifold with o…
On Lewy extension for smooth hypersurfaces in
Jiri Lebl, Alan Noell, Sivaguru Ravisankar
We prove an analogue of the Lewy extension theorem for a real dimension smooth submanifold , . A theorem of Hill and Tai…
Codimension two CR singular submanifolds and extensions of CR functions
Jiri Lebl, Alan Noell, Sivaguru Ravisankar
Let , , be a real codimension two CR singular real-analytic submanifold that is nondegenerate and holomorphically flat. We prove that every…
A note on smoothing properties of the Bergman projection
Sivaguru Ravisankar, Yunus E. Zeytuncu
Recently Herbig, McNeal, and Straube have showed that the Bergman projection of conjugate holomorphic functions is smooth up to the boundary on a class of pseudoconvex domains. We…
Extension of CR functions from boundaries in
Jiri Lebl, Alan Noell, Sivaguru Ravisankar
Let be a bounded domain with smooth boundary such that has only nondegenerate elliptic CR singularities, and let $f \colon…
Tangential Lipschitz Gain for Holomorphic Functions on Domains of Finite Type
Sivaguru Ravisankar
Functions that are holomorphic and Lipschitz in a smoothly bounded domain enjoy a gain in the order of Lipschitz regularity in the complex tangential directions near the boundary.…
Transversally Lipschitz Harmonic Functions are Lipschitz
Sivaguru Ravisankar
Let Ω\subset\mathbb{R}^n be a bounded domain with C^\infty boundary. We show that a harmonic function in Ωthat is Lipschitz along a family of curves transversal to bΩis Lipschitz i…