Related papers: Entire curves producing distinct Nevanlinna curren…

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 the Gelfand problem with rapidly growing nonlinearities in the two-dimensional bounded strictly convex domains. In this paper, we prove the uniformly boundedness of finite Morse index solutions. As a result, we show that there…

We derive the complete supergravity description of the N=2 scalar potential which realizes a generic flux-compactification on a Calabi-Yau manifold (generalized geometry). The effective potential V_{eff}=V_{(\partial_Z V=0)}$, obtained by…

We analyse the possible ways of gluing twisted products of circles with asymptotically cylindrical Calabi-Yau manifolds to produce manifolds with holonomy G_2, thus generalising the twisted connected sum construction of Kovalev and Corti,…

Understanding complexity in fluid mechanics is a major problem that has attracted the attention of physicists and mathematicians during the last decades. Using the concept of renormalization in dynamics, we show the existence of a locally…

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…

In this paper we consider the evolution of regular closed elastic curves $\gamma$ immersed in $\R^n$. Equipping the ambient Euclidean space with a vector field $\ca:\R^n\rightarrow\R^n$ and a function $f:\R^n\rightarrow\R$, we assume the…

We consider the geometric map $ \mathfrak C$, called Cayleyan, associating to a plane cubic $E$ the adjoint of its dual curve. We show that $ \mathfrak C$ and the classical Hessian map $ \mathfrak H$ generate a free semigroup. We begin the…

This is the first part of a series of three papers. In this paper, we establish a Big Picard type theorem for holomorphic maps $f:Y \to X$, where $Y$ is a ramified covering of the punctured disc $\mathbb{D}^*$ with small ramification and…

In this paper we describe a construction which produces classes in a compactification of the moduli space of curves. This construction extends a construction of Kontsevich which produces classes in the open moduli space from the initial…

In this paper, we study a curve flow which preserves the anisotropic length of the evolving curve, and show that for any convex closed initial curve, the flow exists for all time and the evolving curve converges to a homothety of the…

We study the non-perturbative superpotential in E_8 x E_8 heterotic string theory on a non-simply connected Calabi-Yau manifold X, as well as on its simply connected covering space \tilde{X}. The superpotential is induced by the string…

In this paper, we prove that for a given surjective holomorphic endomorphism $f$ of a compact K\"ahler manifold $X$ and for some integer $p$ with $1\le p\le k$, there exists a proper invariant analytic subset $E$ for $f$ such that if $S$ is…

We prove that every acyclic normal one-dimensional real Ambrosio-Kirchheim current in a Polish (i.e. complete separable metric) space can be decomposed in curves, thus generalizing the analogous classical result proven by S. Smirnov in…

We introduce Nevanlinna classes of holomorphic functions associated to a closed set on the boundary of the unit disc in the complex plane and we get Blaschke type theorems relative to these classes by use of several complex variables…

We show that for almost every given symmetry transformation of a Riemannian manifold there exists an eigenvector field of the curl operator, corresponding to a non-zero eigenvalue, which obeys the symmetry. More precisely, given a smooth,…

We construct a compactification of the moduli space of twisted holomorphic maps with varying complex structure and bounded energy. For a given compact symplectic manifold $X$ with a compatible complex structure and a Hamiltonian action of…

We present a new technique to study Jacobian variety decompositions using subgroups of the automorphism group of the curve and the corresponding intermediate covers. In particular, this new method allows us to produce many new examples of…

We consider a regular smooth curve in $\mathbb{E}^n$ such that its coordinates' components are the fundamental solutions of the differential equation $ y^{(n)} (x) - y(x) = 0 ,$ $x \in \mathbb{R} $ of order $n$. We show that the total first…

On a class of compact Hermitian manifolds including compact K\"{a}hler manifolds, we prove that the the relative non-pluripolar product is always well-defined. We also prove the monotonicity of the relative non-pluripolar product in terms…