4 papers
A complex-analytic characterization of Lagrangian immersions in with transverse double points
Purvi Gupta, Rudranil Sahu
Given a compact smooth totally real immersed -submanifold with only finitely many transverse double points, it is known that if is Lagrangian with resp…
A (Hilbert) geometric algorithm for approximating the halfspace depth of a point in a convex body
Purvi Gupta, Anant Narayanan
Halfspace (or Tukey) depth is a fundamental and robust measure of centrality of data points in multivariate datasets. Computing the depth of a point with respect to the uniform dis…
Polynomially convex embeddings and CR singularities of real manifolds
Purvi Gupta, Rasul Shafikov
It is proved that any smooth manifold of dimension admits a smooth polynomially convex embedding into when . Further, such…
Hypersurface Convexity and Extension of Kähler Forms
Blake J. Boudreaux, Purvi Gupta, Rasul Shafikov
The following generalization of a result of S. Nemirovski is proved: if is either a projective or a Stein manifold and is a compact sublevel set of a strictly plur…