ترغب بنشر مسار تعليمي؟ اضغط هنا

First eigenvalue of the $p$-Laplacian on Kahler manifolds

67   0   0.0 ( 0 )
 نشر من قبل Shoo Seto
 تاريخ النشر 2018
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

We prove a Lichnerowicz type lower bound for the first nontrivial eigenvalue of the $p$-Laplacian on Kahler manifolds. Parallel to the $p = 2$ case, the first eigenvalue lower bound is improved by using a decomposition of the Hessian on Kahler manifolds with positive Ricci curvature.

قيم البحث

اقرأ أيضاً

83 - Shoo Seto 2019
we introduce a generalization of the $p$-Laplace operator to act on differential forms and generalize an estimate of Gallot-Meyer for the first nonzero eigenvalue on closed Riemannian manifolds.
122 - Shoo Seto , Guofang Wei 2017
We give various estimates of the first eigenvalue of the $p$-Laplace operator on closed Riemannian manifold with integral curvature conditions.
75 - A. Derdzinski 2002
A special Kahler-Ricci potential on a Kahler manifold is any nonconstant $C^infty$ function $tau$ such that $J( ablatau)$ is a Killing vector field and, at every point with $dtau e 0$, all nonzero tangent vectors orthogonal to $ ablatau$ and $J( abla tau)$ are eigenvectors of both $ abla dtau$ and the Ricci tensor. For instance, this is always the case if $tau$ is a nonconstant $C^infty$ function on a Kahler manifold $(M,g)$ of complex dimension $m>2$ and the metric $tilde g=g/tau^2$, defined wherever $tau e 0$, is Einstein. (When such $tau$ exists, $(M,g)$ may be called {it almost-everywhere conformally Einstein}.) We provide a complete classification of compact Kahler manifolds with special Kahler-Ricci potentials and use it to prove a structure theorem for compact Kahler manifolds of any complex dimension $m>2$ which are almost-everywhere conformally Einstein.
In a paper by Angella, Otal, Ugarte, and Villacampa, the authors conjectured that on a compact Hermitian manifold, if a Gauduchon connection other than Chern or Strominger is Kahler-like, then the Hermitian metric must be Kahler. They also conjecture d that if two Gauduchon connections are both Kahler-like, then the metric must be Kahler. In this paper, we discuss some partial answers to the first conjecture, and give a proof to the second conjecture. In the process, we discovered an interesting `duality phenomenon amongst Gauduchon connections, which seems to be intimately tied to the question, though we do not know if there is any underlying reason for that from physics.
143 - Andrei Moroianu 2009
The moduli space NK of infinitesimal deformations of a nearly Kahler structure on a compact 6-dimensional manifold is described by a certain eigenspace of the Laplace operator acting on co-closed primitive (1,1) forms. Using the Hermitian Laplace ope rator and some representation theory, we compute the space NK on all 6-dimensional homogeneous nearly Kahler manifolds. It turns out that the nearly Kahler structure is rigid except for the flag manifold F(1,2)=SU_3/T^2, which carries an 8-dimensional moduli space of infinitesimal nearly Kahler deformations, modeled on the Lie algebra su_3 of the isometry group.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا