Related papers: RC-positivity and the generalized energy density I…

The variational theory of higher-power energy is developed for mappings between Riemannian manifolds, and more generally sections of submersions of Riemannian manifolds, and applied to sections of Riemannian vector bundles and their sphere…

We propose a generalization of the so-called rational map ansatz on the Euclidean space $\mathbb{R}^3$, for any compact simple Lie group $G$ such that $G/{\widehat K}\otimes U(1)$ is an Hermitian symmetric space, for some subgroup…

Using Polyakov's functional integral approach with the Liouville action functional defined in \cite{ZT2} and \cite{LTT}, we formulate quantum Liouville theory on a compact Riemann surface X of genus g > 1. For the partition function <X> and…

For a Riemannian foliation $F$ on a compact manifold $M$ with a bundle-like metric, the de Rham complex of $M$ is $C^{\infty}$-splitted as the direct sum of the basic complex and its orthogonal complement. Then the basic component…

Fifty years ago, Eells and Sampson have proved a famous theorem in which they argued that any harmonic mapping $f:(M,g) \rightarrow (\bar{M},\bar{g})$ is totally geodesic if $(M, g)$ is a compact manifold with the nonnegative Ricci tensor…

Let $L$ be a (semi)-positive line bundle over a Kahler manifold, $X$, fibered over a complex manifold $Y$. Assuming the fibers are compact and non-singular we prove that the hermitian vector bundle $E$ over $Y$ whose fibers over points $y$…

Let L be an ample holomorphic line bundle over a compact complex Hermitian manifold X. Any fixed smooth Hermitian metric on L induces a Hilbert space structure on the space of global holomorphic sections with values in the k:th tensor power…

We describe some sufficient conditions, under which smooth and compactly supported functions are or are not dense in the fractional Sobolev space $W^{s,p}(\Omega)$ for an open, bounded set $\Omega\subset\mathbb{R}^{d}$. The density property…

We extend an $L^2$ energy gap result due independently to Min-Oo and Parker (1982) for Yang-Mills connections on principal $G$-bundles, $P$, over closed, connected, four-dimensional, oriented, smooth manifolds, $X$, from the case of…

In this paper, we first study the $\alpha-$energy functional, Euler-Lagrange operator and $\alpha$-stress energy tensor. Second, it is shown that the critical points of $\alpha-$ energy functional are explicitly related to harmonic maps…

We prove a Theorem on homotheties between two given tangent sphere bundles $S_rM$ of a Riemannian manifold $M,g$ of $\dim\geq 3$, assuming different variable radius functions $r$ and weighted Sasaki metrics induced by the conformal class of…

We identify the holomorphic de Rham complex of the minimal extension of a meromorphic vector bundle with connexion on a compact Riemann surface X with the L^2 complex relative to a suitable metric on the bundle and a complete metric on the…

We show that on any smooth compact connected manifold of dimension $m\geq 2$ admitting a smooth non-trivial circle action $\mathcal{S} = \left\{S_t\right\}_{t \in \mathbb{R}}$, $S_{t+1}=S_t$, the set of weakly mixing…

This thesis consists of two parts which share only a slight overlap. The first part is concerned with the study of ideals in the ring $C^\infty(M,R)$ of smooth functions on a compact smooth manifold M or more generally submodules of a…

It is well known that a foliation F of a smooth manifold M gives rise to a rich cohomological theory, its characteristic (i.e., leafwise) cohomology. Characteristic cohomologies of F may be interpreted, to some extent, as functions on the…

In this note, we answer positively a question by Belegradek and Kapovitch about the relation between rational homotopy theory and a problem in Riemannian geometry which asks that total spaces of which vector bundles over compact nonnegative…

Let f : X --> Y be a holomorphic map of complex manifolds, which is proper, Kahler, and surjective with connected fibers, and which is smooth over Y-Z the complement of an analytic subset Z. Let E be a Nakano semi-positive vector bundle on…

The main result of this paper is the following: any `weighted' Riemannian manifold $(M,g,\mu)$ - i.e. endowed with a generic non-negative Radon measure $\mu$ - is `infinitesimally Hilbertian', which means that its associated Sobolev space…

Some properties of $m$-density points and density-degree functions are studied. Moreover the following main results are provided: \vskip2mm \begin{itemize} \item {\it Let $\lambda$ be a continuous differential form of degree $h$ in…

We consider radially symmetric, energy critical wave maps from (1 + 2)-dimensional Minkowski space into the unit sphere $\mathbb{S}^m$, $m \geq 1$, and prove global regularity and scattering for classical smooth data of finite energy. In…