Related papers: An elliptic second main theorem
Using an elementary argument, we prove new fixed point theorems for classical elliptic complexes. We obtain new results for conformal relations and coisotropic intersections. We obtain theorems for the average intersections of families of…
The purpose of this paper has twofold. The first is to establish a second main theorem with truncated counting functions for algebraically nondegenerate meromorphic mappings into an arbitrary projective variety intersecting a family of…
This paper deals with elliptic equations in the plane with degeneracies. The equations are generated by a complex vector field that is elliptic everywhere except along a simple closed curve. Kernels for these equations are constructed.…
We establish a second main theorem for algebraic tori with slow growth moving targets with truncation to level 1. As the first application of this result, we prove the Green-Griffith-Lang conjecture for projective spaces with $n+1$…
Let $\mathbf{K}$ be an algebraically closed field of arbitrary characteristic, complete with respect to a non-archimedean absolute value $|\,|$. We establish a Second Main Theorem type estimate for analytic map $f\colon…
We give an elementary proof of the Mazur-Tate-Teitelbaum conjecture for elliptic curves by using Kato's element.
We prove several extensions of the Erdos-Fuchs theorem.
The ellipsoidal superpotential of the complex projective plane can be interpreted as a count of rigid rational plane curves of a given degree with one prescribed cusp singularity. In this note we present a closed formula for these counts as…
We use Beltrami's theorem as an excuse to present some arguments from parabolic differential geometry without any of the parabolic machinery.
This is the second part of a series devoting to the generalizations and applications of common theorems in variational bifurcation theory. Using abstract theorems in the first part we obtain many new bifurcation results for quasi-linear…
A periodic connection is constructed for a double well potential defined in the plane. This solution violates Modica's estimate as well as the corresponding Liouville Theorem for general phase transition potentials. Gradient estimates are…
Our goal in the present paper is to give a new ergodic proof of a well-known Veech's result, build upon our previous works.
We prove a Meyers type regularity estimate for approximate solutions of second order elliptic equations obtained by Galerkin methods. The proofs rely on interpolation results for Sobolev spaces on graphs. Estimates for second order elliptic…
We prove a generalization of one of Lie's Theorems in the context of Lie-like algebras$^{2-nd}$.
We study the critical points of the solution of second elliptic equations in divergence and diagonal form with a bounded and positive definite coefficient, under the assumption that the statement of the Hopf lemma holds (sign assumptions on…
Some symmetry problems are formulated and solved. New simple proofs are given for the earlier studied symmetry problems.
We prove a flat strip theorem for 2-dimensional ptolemaic spaces.
The classification of projective elliptic line scrolls with the description of their singular loci is given. In particular we recover Atiyah Theorem by using classical methods.
This second part is devoted to the proof of all main results that we have mentionned in [KI].
We prove doubling inequalities for solutions of elliptic systems with an iterated Laplacian as diagonal principal part and for solutions of the Lame' system of isotropic linearized elasticity. These inequalities depend on global properties…