Do you want to publish a course? Click here

A Simple Proof for the Generalized Frankel Conjecture

322   0   0.0 ( 0 )
 Added by Xi-Ping Zhu
 Publication date 2007
  fields
and research's language is English
 Authors Hui-Ling Gu




Ask ChatGPT about the research

In this short paper, we will give a simple and transcendental proof for Moks theorem of the generalized Frankel conjecture. This work is based on the maximum principle in cite{BS2} proposed by Brendle and Schoen.

rate research

Read More

In this paper, we will give an extension of Moks theorem on the generalized Frankel conjecture under the condition of the orthogonal bisectional curvature.
Given any admissible $k$-dimensional family of immersions of a given closed oriented surface into an arbitrary closed Riemannian manifold, we prove that the corresponding min-max width for the area is achieved by a smooth (possibly branched) immersed minimal surface with multiplicity one and Morse index bounded by $k$.
We prove the Singer conjecture for extended graph manifolds and pure complex-hyperbolic higher graph manifolds with residually finite fundamental groups. In real dimension three, where a result of Hempel ensures that the fundamental group is always residually finite, we then provide a Price type inequality proof of a well-known result of Lott and Lueck. Finally, we give several classes of higher graph manifolds which do indeed have residually finite fundamental groups.
110 - T. Royen 2014
An extension of the Gaussian correlation conjecture (GCC) is proved for multivariate gamma distributions (in the sense of Krishnamoorthy and Parthasarathy). The classical GCC for Gaussian probability measures is obtained by the special case with one degree of freedom.
We present a proof of the compositional shuffle conjecture, which generalizes the famous shuffle conjecture for the character of the diagonal coinvariant algebra. We first formulate the combinatorial side of the conjecture in terms of certain operators on a graded vector space $V_*$ whose degree zero part is the ring of symmetric functions $Sym[X]$ over $mathbb{Q}(q,t)$. We then extend these operators to an action of an algebra $tilde{AA}$ acting on this space, and interpret the right generalization of the $ abla$ using an involution of the algebra which is antilinear with respect to the conjugation $(q,t)mapsto (q^{-1},t^{-1})$.
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