ترغب بنشر مسار تعليمي؟ اضغط هنا

Inverse scattering results for manifolds hyperbolic near infinity

115   0   0.0 ( 0 )
 نشر من قبل David Borthwick
 تاريخ النشر 2009
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

We study the inverse resonance problem for conformally compact manifolds which are hyperbolic outside a compact set. Our results include compactness of isoresonant metrics in dimension two and of isophasal negatively curved metrics in dimension three. In dimensions four or higher we prove topological finiteness theorems under the negative curvature assumption.



قيم البحث

اقرأ أيضاً

Suppose that $(X, g)$ is a conformally compact $(n+1)$-dimensional manifold that is hyperbolic at infinity in the sense that outside of a compact set $K subset X$ the sectional curvatures of $g$ are identically equal to minus one. We prove that the c ounting function for the resolvent resonances has maximal order of growth $(n+1)$ generically for such manifolds.
For a complete, finite volume real hyperbolic n-manifold M, we investigate the map between homology of the cusps of M and the homology of $M$. Our main result provides a proof of a result required in a recent paper of Frigerio, Lafont, and Sisto.
We prove that any arithmetic hyperbolic $n$-manifold of simplest type can either be geodesically embedded into an arithmetic hyperbolic $(n+1)$-manifold or its universal $mathrm{mod}~2$ Abelian cover can.
89 - Ksenia Fedosova 2015
We study the analytic torsion of odd-dimensional hyperbolic orbifolds $Gamma backslash mathbb{H}^{2n+1}$, depending on a representation of $Gamma$. Our main goal is to understand the asymptotic behavior of the analytic torsion with respect to sequenc es of representations associated to rays of highest weights.
82 - L. Andersson , M. Dahl 1997
Rigidity results for asymptotically locally hyperbolic manifolds with lower bounds on scalar curvature are proved using spinor methods related to the Witten proof of the positive mass theorem. The argument is based on a study of the Dirac operator de fined with respect to the Killing connection. The existence of asymptotic Killing spinors is related to the spin structure on the end. The expression for the mass is calculated and proven to vanish for conformally compact Einstein manifolds with conformal boundary a spherical space form, giving rigidity. In the 4-dimensional case, the signature of the manifold is related to the spin structure on the end and explicit formulas for the relevant invariants are given.
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