Do you want to publish a course? Click here

A new proof of a theorem of Petersen

223   0   0.0 ( 0 )
 Added by Yi-Hu Yang
 Publication date 2014
  fields
and research's language is English




Ask ChatGPT about the research

Let $M$ be an $n$-dimensional complete Riemannian manifold with Ricci curvature $ge n-1$. In cite{colding1, colding2}, Tobias Colding, by developing some new techniques, proved that the following three condtions: 1) $d_{GH}(M, S^n)to 0$; 2) the volume of $M$ ${text{Vol}}(M)to{text{Vol}}(S^n)$; 3) the radius of $M$ ${text{rad}}(M)topi$ are equivalent. In cite{peter}, Peter Petersen, by developing a different technique, gave the 4-th equivalent condition, namely he proved that the $n+1$-th eigenvalue of $M$ $lambda_{n+1}(M)to n$ is also equivalent to the radius of $M$ ${text{rad}}(M)topi$, and hence the other two. In this note, we give a new proof of Petersens theorem by utilizing Coldings techniques.



rate research

Read More

148 - Xiaochun Rong 2019
We will present a new proof for the Gromovs theorem on almost flat manifolds ([Gr], [Ru]).
62 - Florian K. Richter 2020
Let $Omega(n)$ denote the number of prime factors of $n$. We show that for any bounded $fcolonmathbb{N}tomathbb{C}$ one has [ frac{1}{N}sum_{n=1}^N, f(Omega(n)+1)=frac{1}{N}sum_{n=1}^N, f(Omega(n))+mathrm{o}_{Ntoinfty}(1). ] This yields a new elementary proof of the Prime Number Theorem.
In this note we consider submersions from compact manifolds, homotopy equivalent to the Eschenburg or Bazaikin spaces of positive curvature. We show that if the submersion is nontrivial, the dimension of the base is greater than the dimension of the fiber. Together with previous results, this proves the Petersen-Wilhelm Conjecture for all the known compact manifolds with positive curvature.
We give a general method of extending unital completely positive maps to amalgamated free products of C*-algebras. As an application we give a dilation theoretic proof of Bocas Theorem.
229 - Bruce Kleiner 2007
We give a new proof of Gromovs theorem that any finitely generated group of polynomial growth has a finite index nilpotent subgroup. Unlike the original proof, it does not rely on the Montgomery-Zippin-Yamabe structure theory of locally compact groups.
comments
Fetching comments Fetching comments
Sign in to be able to follow your search criteria
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا