5 papers
Rarity of solutions to the complex Monge--Ampère equation on weakly pseudoconvex domains
Gautam Bharali, Rumpa Masanta
We show that on any weakly pseudoconvex -regular domain, the classical Dirichlet problem for the complex Monge--Ampère equation with -smooth data does not i…
Non-smooth paths having unit speed with respect to the Kobayashi metric, and their applications
Gautam Bharali, Rumpa Masanta
We investigate the question of whether a non-constant absolutely continuous path can be reparametrized to be of unit speed with respect to the Kobayashi metric and be absolutely co…
On some connections between Kobayashi geometry and pluripotential theory
Gautam Bharali, Rumpa Masanta
In this paper, we explore some connections between Kobayashi geometry and the Dirichlet problem for the complex Monge--Ampère equation. Among the results we obtain through these c…
Visibility domains relative to the Kobayashi distance in complex manifolds
Rumpa Masanta
In this paper, we extend the notion of visibility relative to the Kobayashi distance to domains in arbitrary complex manifolds. Visibility here refers to a property resembling visi…
Taut visibility domains are not necessarily Kobayashi complete
Rumpa Masanta
We answer a question asked recently by Banik in the negative by showing that for each , there exists a taut visibility domain in that is not Kobayashi compl…