Related papers: An elliptic second main theorem
The paper aims at constructing two different solutions to an elliptic system $$ u \cdot \nabla u + (-\Delta)^m u = \lambda F $$ defined on the two dimensional torus. It can be viewed as an elliptic regularization of the stationary Burgers…
It is proved that the rank of an elliptic curve is one less the arithmetic complexity of the corresponding non-commutative torus. As an illustration, we consider a family of elliptic curves with complex multiplication.
This paper proves a generalization of the Butterfly Theorem, a classical Euclidean result, which is valid in the complex projective plane.
The double-layer potential plays an important role in solving boundary value problems for elliptic equations. All the fundamental solutions of the generalized bi-axially symmetric Helmholtz equation were known, and only for the first one…
We establish the solvability of second order divergence type parabolic systems in Sobolev spaces. The leading coefficients are assumed to be only measurable in one spatial direction on each small parabolic cylinder with the spatial…
We formulate and prove a weighted version of Zariski's hyperplane section theorem on the topological fundamental groups of the complements of hypersurfaces in a projective space. As an application, we calculate fundamental groups of the…
We formulate a second adjoint theorem in the context of tempered representations of real reductive groups, and prove it in the case of SL(2,R).
We present a geometric proof for the duality theorem of linear programming. Besides being self-contained and simple, the present approach also provides a transparent way for understanding this fundamental result.
In this paper we construct layer potentials for elliptic differential operators using the Lax-Milgram theorem, without recourse to the fundamental solution; this allows layer potentials to be constructed in very general settings. We then…
We generalize certain arguments in Zariski's irregularity theorem on cyclic multiple planes.
We prove a generalization of a result of Peres and Schlag on the dimensions of certain exceptional sets of projections and then apply it to a geometric problem.
In this paper, making use of Theorem 2 of [5], we establish a new four critical points theorem which can be regarded as a companion to Theorem 1 of [4]. We also present an application to the Dirichlet problem for a class of quasilinear…
We reprove the strong Hanani-Tutte theorem on the projective plane. In contrast to the previous proof by Pelsmajer, Schaefer and Stasi, our method is constructive and does not rely on the characterization of forbidden minors, which gives…
This paper develops an analytical approach to the study of the geometry of projective maps using the theory of elliptic differential operators. We construct two elliptic operators of second and fourth order, whose kernels characterize…
In this paper we develop a Fefferman-Stein theorem, a Hardy-Littlewood theorem and sharp function estimations in weighted Sobolev spaces. We also provide uniqueness and existence results for second-order elliptic and parabolic partial…
A projective rectangle is like a projective plane that has different lengths in two directions. We develop the basic theory of projective rectangles including incidence properties, projective subplanes, configuration counts, a partial…
We present two new constructions in the usual euclidean plane. We only deal with 'Grecian Geometry', with this phrase we mean elementary geometry in the two-dimensional space R 2 . We describe and prove two propositions about 'projections'.…
We proove a Bloch's theorem in an almost complex projective plane.
In this paper, we establish a second main theorem for holomorphic curve intersecting hypersurfaces in general position in projective space with level of truncation. As an application, we reduce the number hypersurfaces in uniqueness problem…
We give a stack-theoretic proof for some results on families of hyperelliptic curves.