相关论文: Beltrami's theorem via parabolic geometry

In this paper, a new type of comparison theorem is presented for some initial-boundary value problems of second order nonlinear parabolic systems with nonlinear boundary conditions. This comparison theorem has an advantage over the…

We obtain a Bernstein theorem for special Lagrangian graphs in n-dimensional complex space for arbitrary n only assuming bounded slope, but no quantitative restriction.

We present a new proof of the Joints Theorem without taking derivatives. Then we generalize the proof to prove the Multijoints Conjecture and Carbery's generalization. All results are in any dimension over an arbitrary field.

A new and easy way of deriving Gauss's Generalized Hypergeometric Theorem is presented by using the Bilateral Binomial Theorem.

The theory of plasma physics offers a number of nontrivial examples of partial differential equations, which can be successfully treated with symmetry methods. We propose three different examples which may illustrate the reciprocal…

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.

We give a simple proof of Dorronsoro's theorem and use similar ideas to establish an equivalence for embeddings of vector fields.

The purpose of this paper is fourfold. The first is to develop the theory of tropical differential algebraic geometry from scratch; the second is to present the tropical fundamental theorem for differential algebraic geometry, and show how…

This is an expository paper in which we explain how basic, standard, results about simple Lie algebras can be obtained by geometric arguments, following ideas of Cartan, Richardson and others.

There are several proofs of the Fundamental Theorem of Algebra, mainly using algebra, analysis and topology. In this article, we have shown that the Fundamental Theorem of Algebra can be proved using Nevanlinna's first fundamental theorem…

In this paper, we present the Baumkuchen Theorem related to the combination of divided Baumkuchen pieces. It can be proved using the basic properties of elementary geometry. We also apply some lemmas to prove the Pizza Theorem.

Understanding geometric relationships with little mathematical knowledge can be challenging for today's students and teachers. A new toolset is introduced that is able to create a proof without words by combining the benefits of the…

We establish a relative Bertini type theorem for multiplier ideal sheaves. Then we prove a relative version of the Koll\'ar--Nadel type vanishing theorem as an application.

In this note, we will explain the connection between the Seven Circles Theorem and hyperbolic geometry, then prove a stronger result about hyperbolic geometry hexagons which implies the Seven Circles Theorem as a special case.

We prove a singular version of the Engel theorem. We prove a normal form theorem for germs of holomorphic singular Engel systems with good conditions on its singular set. As an application, we prove that there exists an integral analytic…

This paper presents an alternative proof of the Fundamental Theorem of Algebra that has several distinct advantages. The proof is based on simple ideas involving continuity and differentiation. Visual software demonstrations can be used to…

A notion of an algebroid - a generalization of a Lie algebroid structure is introduced. We show that many objects of the differential calculus on a manifold M associated with the canonical Lie algebroid structure on T^M can be obtained in…

We prove a second main theorem for elliptic projective planes.

Eberhard-type theorems are statements about the realizability of a polytope (or more general polyhedral maps) given the valency of its vertices and sizes of its polygonal faces up to a linear linear degree of freedom. We present new…

We present an alternative proof of Perron's theorem, which is probabilistic in nature. It rests on the representation of the Perron eigenvector as a functional of the trajectory of an auxiliary Markov chain.