Related papers: A relative Toponogov comparison theorem

We prove a version of Dedekind's Transposition Principle that holds in lattices of equivalence relations.

In this article we give a result obtained of an experimental way for the Euler totient function.

We proove a Bloch's theorem in an almost complex projective plane.

We define a relative version of contact homology for contact manifolds with convex boundary, and prove basic properties of this relative contact homology. Similar considerations also hold for embedded contact homology.

We survey the classical results on the prime number theorem

We prove a variation of Gronwall's lemma.

In this note we briefly survey and propose some open problems related to isoparametric theory.

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 convergence theorem for partial sums of sectorial forms with vertex zero and a common semi-angle. As an example we prove an absorption theorem for sectorial forms.

We give a short and relatively elementary proof of the Hilton-Milner Theorem.

In this paper, we define an ordering relation for a set of complex numbers, and research the properties and theorems of the ordering, solve some simple complex inequalities with the ordering.

We discuss the (twisted) weak positivity theorem. We also treat some applications.

In this paper, we introduce a thinness in sense to a type of relative capacity for weighted variable exponent Sobolev space. Moreover, we reveal some properties of this thinness and consider the relationship with finely open and finely…

In this article, we introduce an interesting topology-like concept concerning groups (and with almost the same method it can be defined for other algebraic systems). Given an arbitrary group $G$, we define a {\em topo-system} on $G$ as a…

We provide a proof of the sharp log-Sobolev inequality on a compact interval.

We discuss various recent advances on weak forms of the Twin Prime Conjecture.

We prove a connectedness result for products of weighted projective spaces.

We prove several congruences for trinomial coefficients.

We prove Burkholder inequality using Bregman divergence.

A very short proof of G\"odel's second incompleteness theorem (for set theory, second order arithmetic etc.)