Related papers: A short proof of Cramer's theorem in R
In this short exposition we provide a simplified proof of Buser's result for Cheeger's isoperimetric constant.
A one-line proof of a minimax theorem due to Steinerberger is given.
The purpose of this article is to present my new proof of the the construction and the convergence theorem of spectral sequences of filtered complexes, which is much shorter and cleaner than the "standard" proof.
This note rederives a formula for $r$-color partitions, $1 \le r \le 24$, including Rademacher's celebrated result for ordinary partitions, from the duality between modular forms of weights $-r/2$ and $2+r/2$.
We prove several extensions of the Erdos-Fuchs theorem.
The paper contains an alternative proof of M. Kontsevich Formality Theorem.
A simple proof is given for the convexity of log det (I+K X^{-1}) in the positive definite matrix variable X with a given positive semidefinite K.
We prove a general duality theorem for tangle-like dense objects in combinatorial structures such as graphs and matroids. This paper continues, and assumes familiarity with, the theory developed in [6]
We prove splitting theorems for mean convex open subsets in RCD (Riemannian curvature-dimension) spaces that extend results by Kasue, Croke and Kleiner for Riemannian manifolds with boundary to a non-smooth setting. A corollary is for…
We give a counting based proof of the Graham Pollak Theorem
We give a simple direct proof of Fermat's two squares theorem. Our argument uses no intricate notions or ideas; one might say that it is a proof by careful bookkeeping. As such, the proof may be particularly easy to comprehend by students…
We give a proof of some small weight and level cases of Serre's conjecture.
We will present a new proof of the Gromoll-Grove diameter rigidity theorem.
We present a short proof of the Alexandrov-Fenchel inequalities for mixed volumes of convex bodies.
This paper gives a concise proof of the Jordan curve theorem on discrete surfaces. We also embed the discrete surface in the 2D plane to prove the original version of the Jordan curve theorem. This paper is a simple version of L. Chen, Note…
We give a succinct proof of a duality theorem obtained by R\'ev\'esz in 1991 which concerns extremal quantities related to trigonomertic polynomials. The key tool of our new proof is an intersection formula on dual cones in real Banach…
This article presents a clear proof of the Riemann Mapping Theorem via Riemann's method, uncompromised by any appeals to topological intuition.
We prove an extension of a ham sandwich theorem for families of lines in the plane by Dujmovi\'{c} and Langerman. Given two sets $A, B$ of $n$ lines each in the plane, we prove that it is possible to partition the plane into $r$ convex…
We discuss Nakamaye's Theorem and its recent extension to compact complex manifolds, together with some applications.
It is pointed out that current conservation alone does not suffice to prove Hara's theorem as it was claimed recently. By explicit calculation we show that the additional implicit assumption made in such "proofs" is that of a sufficiently…