Related papers: An elliptic second main theorem

We present a new, elementary, dynamical proof of the prime number theorem.

We present simple and direct proof to an important case of Nash-Moser-Ekeland theorem.

In this paper we show an index theorem for gerbes

We establish the second main theorem with the best truncation level one for an entire holomorphic curve $f:\C \to A$ into a semi-abelian variety $A$ and an arbitrary effective reduced divisor $D$ on $A$; the low truncation level is…

We present some results on projective toric varieties which are relevant in Diophantine geometry. We interpret and study several invariants attached to these varieties in geometrical and combinatorial terms. We also give a B\'ezout theorem…

The double-layer potential plays an important role in solving boundary value problems for elliptic equations, and in the study of which for a certain equation, the properties of the fundamental solutions of the given equation are used. All…

We show that Isserlis' theorem follows as a corollary to the invariant tensor theorem for isotropic tensors.

This work is a continuation of [1]. As in the previous article, here we will describe some interesting ideas and a lot of new theorems in plane geometry related to them.

The first part of this note contains a review of basic properties of the variety of lines contained in an embedded projective variety and passing through a general point. In particular we provide a detailed proof that for varieties defined…

Let $E/\mathbf{Q}$ be an elliptic curve and $p\geq 3$ be a prime. We prove the $p$-converse theorems for elliptic curves of potentially good ordinary reduction at Eisenstein primes (i.e., such that the residual representation $E[p]$ is…

We give a concise proof of the fundamental theorem of smoothing theory in the special case when a smoothing exists.

We present in this work a new and simple proof of the false centre theorem.

We obtain a new differentiable sphere theorem for compact Lagrangian submanifolds in complex Euclidean space and complex projective space.

We introduce a new approach for the study of the Problem of Iterates using the theory on general ultradifferentiable structures developed in the last years. Our framework generalizes many of the previous settings including the Gevrey case…

We apply an improvement of the Delsarte LP-bound to give a new proof of the non-existence of finite projective planes of order 6, and uniqueness of finite projective planes of order 7. The proof is computer aided, and it is also feasible to…

We classify the second order, linear, two by two systems for which the two fundamental theorems for planar harmonic mappings, the Rado'-Kneser-Choquet Theorem and the H. Lewy Theorem, hold. They are those which, up to a linear change of…

The solvability in $W^{2}_{p}(\bR^{d})$ spaces is proved for second-order elliptic equations with coefficients which are measurable in one direction and VMO in the orthogonal directions in each small ball with the direction depending on the…

We consider infinite measure-preserving non-primitive self-similar tiling systems in Euclidean space $\mathbb R^d$. We establish the second-order ergodic theorem for such systems, with exponent equal to the Hausdorff dimension of a…

We consider maximum principles and related estimates for linear second order elliptic partial differential operators in n-dimensional Euclidean space, which improve previous results, with H-J Kuo, through sharp Lp dependence on the drift…

We prove that solutions to elliptic equations in two variables in divergence form, possibly non-selfadjoint and with lower order terms, satisfy the strong unique continuation property.