相关论文: Beltrami's theorem via parabolic geometry

We construct variations for the classes of regular solutions to degenerate Beltrami equations with restrictions of the set-theoretic type for the complex coefficient. On this basis, we prove the variational maximum principle and other…

An algebraic technique is presented that does not use results of model theory and makes it possible to construct a general Galois theory of arbitrary nonlinear systems of partial differential equations. The algebraic technique is based on…

For smooth manifolds equipped with various geometric structures, we construct complexes that replace the de Rham complex in providing an alternative fine resolution of the sheaf of locally constant functions. In case that the geometric…

If a (non-constant) polynomial has no zero, then a certain Riemannian metric is constructed on the two dimensional sphere. Several geometric arguments are then shown to contradict this fact.

Wedderburn's theorem on the structure of finite dimensional semisimple algebras is proved by using minimal prerequisites.

We give a proof of Pythagoras' theorem which does not use neither squares nor similarity of triangles.

We give a simple proof of the Fourier Inversion Theorem, using the methods of nonstandard analysis.

We prove a Torelli-like theorem for higher-dimensional function fields, from the point of view of "almost-abelian" anabelian geometry.

This thesis is concerned with the theory of invariant bilinear differential pairings on parabolic geometries. It introduces the concept formally with the help of the jet bundle formalism and provides a detailed analysis. More precisely,…

In this article we present a generalization of a Leibniz's geometrical theorem and an application of it.

A variational proof is provided of the existence and uniqueness of evolutions of regular Lagrangian systems.

Geometric algebra is the natural outgrowth of the concept of a vector and the addition of vectors. After reviewing the properties of the addition of vectors, a multiplication of vectors is introduced in such a way that it encodes the famous…

Paravectors just like integers have a ring structure. By introducing an integrated product we get geometric properties which make paravectors similar to vectors. The concepts of parallelism, perpendicularity and the angle are conceptually…

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 prove an analogue of Belyi's theorem in characteristic two. Our proof consists of the following three steps. We first introduce a new notion called "pseudo-tame" for morphisms between curves over an algebraically closed field of…

We study the interplay between geometry and partial differential equations. We show how the fundamental ideas we use require the ability to correctly calculate the dimensions of spaces associated to the varieties of zeros of the symbols of…

Tropical Differential Algebraic Geometry considers difficult or even intractable problems in Differential Equations and tries to extract information on their solutions from a restricted structure of the input. The Fundamental Theorem of…

We show that a properly convex projective structure $\mathfrak{p}$ on a closed oriented surface of negative Euler characteristic arises from a Weyl connection if and only if $\mathfrak{p}$ is hyperbolic. We phrase the problem as a…

We present a novel derivation of the elastic theory of shells. We use the language of Geometric algebra, which allows us to express the fundamental laws in component-free form, thus aiding physical interpretation. It also provides the tools…

A two-dimensional nonlinear gauge theory that can be proposed for generalization to higher dimensions is derived by means of cohomological arguments.