Related papers: A relative Toponogov comparison theorem
In this paper we generalize the DP framework to a relative DP framework, where a so called split is possible.
We generalize Romanoff's theorem. Also, we obtain a result on sums related to Euler's totient function.
In the paper, we give a Schur-Toponogov theorem in Riemannian geometry, which not only generalizes Schur's and Toponogov's theorem but also indicates their relation. Inspired by its proof, we also supply a new proof of Toponogov's theorem…
A vector variational principle is proved.
We present in this work a new and simple proof of the false centre theorem.
The paper presents a counterexample to the Hodge conjecture.
We give a q-analogue of Gauss' divisibility theorem
Proof systems for the Relativized Propositional Calculus are defined and compared.
We provide a new characterization of the logarithmic Sobolev inequality.
We study some topological properties of attractors.
In this paper, we construct a comparison map from the topological fundamental group to the pro-\'etale fundamental group for a complex variety.
We systematically investigate the functors between sites which induce morphisms of relative toposes. In particualar, we establish a relative version of Diaconescu's theorem, characterizing the relative geometric morphisms towards a relative…
The first version of this paper gave another proof of the Kropholler Conjecture, which gives a relative version of Stallings Ends Theorem, following an earlier incorrect proof. It has been pointed out by Sam Shepherd that the the second…
We give a survey on recent development of the Novikov conjecture and its applications to topological rigidity and non-rigidity. .
We discuss some aspects of the theory of subelliptic estimates.
In this paper, we give a simple counter example to the famous Hodge conjecture.
We discuss several classical and recent proofs of the isoperimetric inequality and the Sobolev inequality.
We prove mean comparison from a different perspective, where we introduce the concept of partial convolution.
In this paper, we prove an inequality regarding the differential polynomial. This improves some recent results.
In this expository note, we present a transparent proof of Toponogov's theorem for Alexandrov spaces in the general case, not assuming local compactness of the underlying metric space. More precisely, we show that if M is a complete…