arXiv subjects

Morris Kalka

Publications and source records attributed to Morris Kalka.

6 recordsLinked to original sources

arXiv2017

Monge-Ampère exhaustions of almost homogeneous manifolds

We consider three fundamental classes of compact almost homogeneous manifolds and show that the complements of singular complex orbits in such manifolds are endowed with plurisubharmonic exhaustions satisfying complex homogeneous Monge-Ampère equations. This extends to a new family of mixed type examples various classical results on parabolic spaces and complexifications of symmetric spaces. Rigidity results on complex spaces modeled on such new examples are given.

math.CV↗

arXiv2014

Splitting Parabolic Manifolds

We study the geometric properties of complex manifolds possessing a pair of plurisubharmonic functions satisfying Monge-Ampère type of condition. The results are applied to characterize complex manifolds biholomorphic to $\C^{N}$ viewed as a product of lower dimensional complex euclidean spaces.

math.CV↗

arXiv2014

Locally Monge-Ampere Foliations

It is shown that codimension one parabolic foliations of complex manifolds are holomorphic. This is proved using the fact that codimension one foliations of complex manifolds are necessarily locally Monge-Ampère foliations and that parabolic leaves cannot have hyperbolic behavior. The result holds true also for locally Monge-Ampère foliations with parabolic leaves of arbitrary codimension.

math.CV↗

arXiv2009

Monge-Ampere foliations for degenerate solutions

We study the problem of the existence and the holomorphicity of the Monge-Ampère foliation associated to a plurisubharmonic solutions of the complex homogeneous Monge-Ampère equation even at points of arbitrary degeneracy. We obtain good results for real analytic unbounded solutions. As a consequence we also provide a positive answer to a question of Burns on homogeneous polynomials whose logarithm satisfies the complex Monge-Ampère equation and we obtain a generalization the work of P.M. Wong on the classification of complete weighted circular domains.

math.CV↗

arXiv2008

Finite Type Monge-Ampère Foliations

In this paper we extend our previous work on singularities of Monge-Ampère foliations to the case of pseudoconvex finite type domains. We are able to answer the questin of Burns on homogeneous polynomials whose logarithm satisfies the complex Monge-Ampère equation completely in dimension 2 . We are also able to generalize the work of P.M. Wong in dimension 2 on the classification of complete weighted circular domains to include finite type domains.

math.CV↗

arXiv2002

Singular Monge-Ampere foliations

This replaces the previous version, by correcting an error in the proof of Theorem 1.4, that was pointed out by the referee.

math.CV↗