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Mohan Ramachandran

Publications and source records attributed to Mohan Ramachandran.

8 recordsLinked to original sources
arXiv2017

A cup product lemma for continuous plurisubharmonic functions

A version of Gromov's cup product lemma in which one factor is the (1,0)-part of the differential of a continuous plurisubharmonic function is obtained. As an application, it is shown that a connected noncompact complete Kaehler manifold that has exactly one end and admits a continuous plurisubharmonic function that is strictly plurisubharmonic along some germ of a 2-dimensional complex analytic set at some point has the Bochner-Hartogs property; that is, the first compactly supported cohomology with values in the structure sheaf vanishes.

math.CV↗
arXiv2009

Fill Radius and the Fundamental Group

In this note we relate the geometric notion of fill radius with the fundamental group of the manifold. We prove: ''Suppose that a closed Riemannian manifold M satisfies the property that its universal cover has bounded fill radius. Then the fundamental group of M is virtually free.'' We explain the relevance of this theorem to some conjectures on positive isotropic curvature and 2-positive Ricci curvature.

math.DG↗
arXiv2009

Linear Shafarevich Conjecture

We prove that the universal covering space of a complex projective manifold is holomorphically convex provided its fundamental group is linear.

math.AG↗
arXiv2007

L^2 Castelnuovo-de Franchis, the cup product lemma, and filtered ends of Kaehler manifolds

Simple approaches to the proofs of the L^2 Castelnuovo-de Franchis theorem and the cup product lemma which give new versions are developed. For example, suppose u and v are two linearly independent closed holomorphic 1-forms on a bounded geometry connected complete Kaehler manifold X with v in L^2. According to a version of the L^2 Castelnuovo-de Franchis theorem obtained in this paper, if u and v are pointwise linearly dependent, then there exists a surjective proper holomorphic mapping of X onto a Riemann surface for which u and v are pull-backs. Previous versions required both forms to be in L^2.

math.DG↗
arXiv2006

Filtered ends, proper holomorphic mappings of Kahler manifolds to Riemann surfaces, and Kahler groups

The main goal of this paper is to prove that a connected bounded geometry complete Kahler manifold which has at least 3 filtered ends admits a proper holomorphic mapping onto a Riemann surface. This also provides a different proof of the theorem of Gromov and Schoen that, for a connected compact Kahler manifold whose fundamental group admits a proper amalgamated product decomposition, some finite unramified cover admits a surjective holomorphic mapping onto a curve of genus at least 2. The main results are also used to show that any properly ascending HNN extension with finitely generated base group, as well as Thompson's groups V, T, and F, are not Kahler. This version contains details which will not appear in a version submitted for publication.

math.DG↗
arXiv2005

Thompson's Group F is Not Kahler

The purpose of this note is to prove that Richard Thompson's group F and variants of it studied by Ken Brown are not Kahler groups.

math.GR↗
arXiv2004

Elementary construction of subharmonic exhaustion functions

By a theorem of Greene and Wu, a noncompact connected Riemannian manifold admits a smooth strictly subharmonic exhaustion function. Demailly provided an elementary proof of this fact. A further simplification of Demailly's proof and some (mostly known) applications are described. Applications include the fact that the holomorphic line bundle associated to a nontrivial effective divisor on a compact connected complex manifold admits a smooth Hermitian metric with positive scalar curvature.

math.DG↗