Rumpa Masanta

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math.CV2026

Rarity of $C^{1, 1}$ solutions to the complex Monge--AmpÃ¨re equation on weakly pseudoconvex domains

Gautam Bharali, Rumpa Masanta

We show that on any weakly pseudoconvex $B$ -regular domain, the classical Dirichlet problem for the complex Monge--AmpÃ¨re equation with $C^{\infty}$ -smooth data does not i…

math.CV2025

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--AmpÃ¨re equation. Among the results we obtain through these c…

math.CV2025

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…

math.CV2025

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 $n \geq 2$ , there exists a taut visibility domain in $C^{n}$ that is not Kobayashi compl…

Rarity of C1,1 solutions to the complex Monge--AmpÃ¨re equation on weakly pseudoconvex domains

On some connections between Kobayashi geometry and pluripotential theory

Visibility domains relative to the Kobayashi distance in complex manifolds

Taut visibility domains are not necessarily Kobayashi complete

Rarity of $C^{1, 1}$ solutions to the complex Monge--AmpÃ¨re equation on weakly pseudoconvex domains