Related papers: Nakamaye's theorem on complex manifolds
We explain a correct proof of the decomposition theorem for direct images of constant Hodge modules by proper K\"ahler morphisms of complex manifolds. We also give some examples showing certain difficulty in the non-constant Hodge module…
In this article, we develop a new index theory for noncompact manifolds endowed with an admissible exhaustion by compact sets. This index theory allows us to provide examples of noncompact manifolds with exotic positive scalar curvature…
We prove the several variable version of the classical equidistribution theorem for Fekete points of a compact subset of the complex plane, which settles a well-known conjecture in pluri-potential theory. The result is obtained as a special…
We prove the existence of a solution of the Yamabe equation on complete manifolds with finite volume and positive Yamabe invariant. In order to circumvent the standard methods on closed manifolds which heavily rely on global (compact)…
We propose a conjecture on integrality property of the open-closed mirror maps of compact Calabi-Yau manifolds. Some examples are presented.
The main purpose of this paper is to introduce a new smooth version of a CW complex named a fat CW complex, and to show that it includes all closed manifolds, because existing smooth versions of CW complexes (e.g. [Iwa22]) do not have such…
We use Gromov's K--area to define a generalized homology theory on compact smooth manifolds. In fact, this theory collects obstructions to the enlargeability of the manifold and its nontrivial submanifolds. Moreover, using the K--area…
We construct a simple finite-dimensional topological quantum field theory for compact 3-manifolds with triangulated boundary.
We introduce a new class of singular complex manifolds and we develop a degenerate Kodaira-Hodge theory for this class of singular manifolds.
We prove the Nagata compactification theorem for any separated map of finite type between quasi-compact and quasi-separated algebraic spaces, generalizing earlier results of Raoult. Along the way we also prove (and use) absolute noetherian…
In this paper we present a Kakutani type theorem that is equivalent to the Borsuk--Ulam theorem for manifolds.
We introduce a proximal subdifferential and develop a calculus for nonsmooth functions defined on any Riemannian manifold $M$. We give several applications of this theory, concerning: 1) differentiability and geometrical properties of the…
In this paper we show that Mergelyan's theorem holds for maps from open Riemann surfaces to Oka manifolds. This is used to prove the analogue of Arakelian's theorem on uniform approximation of holomorphic maps from closed subsets of the…
In this paper, we establish a Gauss-Bonnet-Chern theorem for general closed complex Finsler manifolds.
We generalize the classical Blaschke Rolling Theorem to convex domains in Riemannian manifolds of bounded sectional curvature and arbitrary dimension. Our results are sharp and, in this sharp form, are new even in the model spaces of…
Haga's fold in paper folding is generalized. Recent generalization of Haga's theorems and problems in Wasan geometry involving Haga's fold are also generalized.
Here we simplify the proof of the de Rham theorem for Schwartz functions on affine Nash manifolds and generalize the result to the case of non affine Nash manifolds.
The purpose of this note is to give an (esentially optimal) effective version of Matsusaka's Big theorem for smooth projective surfaces.
The KAM iterative scheme turns out to be effective in many problems arising in perturbation theory. I propose an abstract version of the KAM theorem to gather these different results.
In this paper, we study compact complex orbifolds. In the first part, we shows the equivalence of two notions of compact K\"ahler orbifold. In the second part, we shows various versions of Demailly's regularisation theorems for compact…