Related papers: On holomorphic functions on negatively curved mani…

In this short note we prove that a Kahler manifold with lower Ricci curvature bound and almost maximal volume is Gromov-Hausdorff close to the projective space with the Fubini-Study metric. This is done by combining the recent results of…

We study geometry, topology and deformation spaces of noncompact complex hyperbolic manifolds (geometrically finite, with variable negative curvature), whose properties make them surprisingly different from real hyperbolic manifolds with…

In this note we consider the following conjecture: given any closed symplectic manifold $M$, there is a sufficiently small real positive number $\rho$ such that the open ball of radius $\rho$ in the Hofer metric centered at the identity on…

Let $(\M^n, g)$ be a $n$ dimensional, complete ( compact or noncompact) Riemannian manifold whose Ricci curvature is bounded from below by a constant $-K \le 0$. Let $u$ be a positive solution of the heat equation on $\M^n \times (0,…

We consider complete non-compact manifolds with either a sub-quadratic growth of the norm of the Riemann curvature, or a sub-quadratic growth of both the norm of the Ricci curvature and the squared inverse of the injectivity radius. We show…

We prove that various spaces of constrained positive scalar curvature metrics on compact 3-manifolds with boundary, when not empty, are contractible. The constraints we mostly focus on are given in terms of local conditions on the mean…

For asymptotically hyperbolic manifolds of dimension $n$ with scalar curvature at least equal to $-n(n-1)$ the conjectured positive mass theorem states that the mass is non-negative, and vanishes only if the manifold is isometric to…

In this paper, we address an extension of the theory of self-concordant functions for a manifold. We formulate the self-concordance of a geodesically convex function by a condition of the covariant derivative of its Hessian, and verify that…

After establishing some new global facts (like a measure theoretic structure theorem and approximation results) about complex-valued functions with bounded variation on arbitrary noncompact Riemannian manifolds, we extend results of…

We prove that the space of smooth Riemannian metrics on the three-ball with non-negative Ricci curvature and strictly convex boundary is path connected; and, moreover, that the associated moduli space (i.e., modulo orientation-preserving…

We derive expressions for the Ricci curvature tensor and scalar in terms of intrinsic torsion classes of half-flat manifolds by exploiting the relationship between half-flat manifolds and non-compact $G_2$ holonomy manifolds. Our…

A notable example due to Heier, Lu, Wong, and Zheng shows that there exist compact complex K\"ahler manifolds with ample canonical line bundle such that the holomorphic sectional curvature is negative semi-definite and vanishes along…

Let $M=X\times Y$ be the product of two complex manifolds of positive dimensions. In this paper, we prove that there is no complete K\"ahler metric $g$ on $M$ such that: either (i) the holomorphic bisectional curvature of $g$ is bounded by…

It is a well-known and elementary fact that a holomorphic function on a compact complex manifold without boundary is necessarily constant. The purpose of the present article is to investigate whether, or to what extent, a similar property…

In this paper we analyze the behavior of the distance function under Ricci flows whose scalar curvature is uniformly bounded. We will show that on small time-intervals the distance function is $\frac12$-H\"older continuous in a uniform…

The paper is concerned with the properties of the distance function from a closed subset of a Riemannian manifold, with particular attention to the set of singularities.

The classical Hadamard three circle theorem is generalized to complete K\"ahler manifolds. More precisely, we show that the nonnegativity of the holomorphic sectional curvature is a necessary and sufficient condition for the three circle…

We provide a general contractibility criterion for subsets of Riemannian metrics on the disc. For instance, this result applies to the space of metrics that have positive Gauss curvature and make the boundary circle convex (or geodesic).…

This article contains a compression of results from alg-geom/9501001, with most proofs omitted. We prove that every two points of the connected moduli space of holomorphically symplectic manifolds can be connected with so-called ``twistor…

For any connected component $H_0$ of the space of real meromorphic functions we build a compactification $N(H_0)$ of the space $H_0$. Then we express the Euler characteristics of the spaces $H_0$ and $N(H_0)$ in terms of topological…