4 papers · 1 filter
The top Yau--Yang conjecture for Kähler manifolds with positive sectional curvature
Ved V. Datar, Vamsi P. Pingali, Harish Seshadri
We prove that the top wedge power of the Ricci form of a complete non-compact Kähler manifold with positive sectional curvature has finite integral. Using a result of Chen-Zhu, an…
Uniformisation of complete Kähler surfaces with positive sectional curvature
Ved Datar, Vamsi Pritham Pingali, Harish Seshadri
We prove that any complete non-compact Kähler surface with positive sectional curvature is biholomorphic to , establishing the two dimensional case of the weaker for…
The complex Monge-Ampere equation and an application to uniformisation of surfaces
Ved Datar, Vamsi Pritham Pingali, Harish Seshadri
We prove that a complete noncompact Kähler surface with positive and bounded sectional curvature is biholomorphic to . This result confirms a special case of Yau's c…
Non-abelian symmetric critical gravitating vortices on a sphere
Vamsi Pritham Pingali
We produce examples of solutions to the non-abelian gravitating vortex equations, which are a dimensional reduction of the Käher-Yang-Mills- Higgs equations. These are equations f…