Related papers: Semilinear equations, the $\gamma_k$ function, and…
In this note, we will present global equisingular approximations of quasi-plurisubharmonic functions with stable analytic pluripolar sets on compact complex manifolds.
In 1977, Gauduchon proved that on every compact hermitian manifold $(X, \omega)$ there exists a conformally equivalent hermitian metric $\omega_{\mathrm{G}}$ which satisfies $\mathrm{dd}^c \omega_{\mathrm{G}}^{n-1} = 0$. In this note, we…
We define the notion of geodesic completeness for semi-Riemannian metrics of low regularity in the framework of the geometric theory of generalized functions. We then show completeness of a wide class of impulsive gravitational wave…
In this article, we investigate the geometry of critical metrics of the volume functional on an $n$-dimensional compact manifold with (possibly disconnected) boundary. We establish sharp estimates to the mean curvature and area of the…
We consider certain examples of applications of the general methods, based on geometry and integrability of matrix models, described in hep-th/0601212. In particular, the nonlinear differential equations, satisfied by quasiclassical…
Let X be a smooth projective Berkovich space over a complete discrete valuation field K of residue characteristic zero, endowed with an ample line bundle L. We introduce a general notion of (possibly singular) semipositive (or…
Let (M,g) be a compact Riemannian manifold of dimension n. For k \in {0,...,n}, we denote Gr_{k}(M) the set of compact, connected and oriented submanifolds of M of dimension k. This set is called the non-linear Grassmannian. In this…
On any metric space, I provide an intrinsic characterization of those complex-valued functions which are uniform limits of Lipschitz functions. There are applications to function theory on complete Riemannian manifolds and, in particular,…
We introduce a class of Hermitian metrics, that we call pluriclosed star split, generalising both the astheno-K\"ahler metrics of Jost and Yau and the $(n-2)$-Gauduchon metrics of Fu-Wang-Wu on complex manifolds. They have links with…
In this paper we consider the prescribed Gauduchon scalar curvature problem on almost Hermitian manifolds. By deducing the expression of the Gauduchon scalar curvature under the conformal variation, the problem is reduced to solve a…
We introduce a countable collection of positivity classes for Hermitian symmetric functions on a complex manifold, and establish their basic properties. We study a related notion of stability. The first main result shows that, if the…
In this note we show that on any compact subdomain of a K\"ahler manifold that admits sufficiently many global holomorphic functions, the products of harmonic functions form a complete set. This gives a positive answer to the linearized…
We introduce the notion of functionally compact sets into the theory of nonlinear generalized functions in the sense of Colombeau. The motivation behind our construction is to transfer, as far as possible, properties enjoyed by standard…
Based on Colombeau's theory of algebras of generalized functions we introduce the concepts of generalized functions taking values in differentiable manifolds as well as of generalized vector bundle homomorphisms. We study their basic…
Given a compact symplectic manifold $M$, with integral symplectic form, we prequantize a certain class of functions on the path space for $M$. The functions in question are induced by functions on $M$. We apply our construction to study the…
The aim of this paper is to study new classes of Riemannian manifolds endowed with a smooth potential function, including in a general framework classical canonical structures such as Einstein, harmonic curvature and Yamabe metrics, and,…
We study the growth of harmonic functions on complete Riemann-ian manifolds where the extrinsic diameter of geodesic spheres is sublinear. It is an generalization of a result of A. Kazue. We also get a Cheng and Yau estimates for the…
We obtain Ricci flat K\"ahler metrics on complex symmetric spaces of rank two by using an explicit asymptotic model whose geometry at infinity is interpreted in the wonderful compactification of the symmetric space. We recover the metrics…
We discuss the construction of toric Kaehler metrics on symplectic 2n-manifolds with a hamiltonian n-torus action and present a simple derivation of the Guillemin formula for a distinguished Kaehler metric on any such manifold. The results…
In the present paper, we study several complex manifolds by using the following idea. First, we construct a certain moduli space and study the fundamental group of this space. This fundamental group is naturally mapped to the groups…