A first eigenvalue estimate for embedded hypersurfaces
نویسندگان
چکیده
منابع مشابه
First stability eigenvalue characterization of Clifford hypersurfaces
ABSTRACT : The stability operator of a compact oriented minimal hypersurface Mn−1 ⊂ S is given by J = −∆ − ‖A‖ − (n − 1), where ‖A‖ is the norm of the second fundamental form. Let λ1 be the first eigenvalue of J and define β = −λ1 − 2(n − 1). In [S] Simons proved that β ≥ 0 for any non-equatorial minimal hypersurface M ⊂ S. In this paper we will show that β = 0 only for Clifford hypersurfaces. ...
متن کاملPinching of the First Eigenvalue for Second Order Operators on Hypersurfaces of the Euclidean Space
We prove stability results associated with upper bounds for the first eigenvalue of certain second order differential operators of divergencetype on hypersurfaces of the Euclidean space. We deduce some applications to r-stability as well as to almost-Einstein hypersurfaces.
متن کاملA Lichnerowicz estimate for the first eigenvalue of convex domains in Kähler manifolds
In this article, we prove a Lichnerowicz estimate for a compact convex domain of a Kähler manifold whose Ricci curvature satisfies Ric ≥ k for some constant k > 0. When equality is achieved, the boundary of the domain is totally geodesic and there exists a nontrivial holomorphic vector field. We show that a ball of sufficiently large radius in complex projective space provides an example of a s...
متن کاملDirac Operator on Embedded Hypersurfaces
New extrinsic lower bounds are given for the classical Dirac operator on the boundary of a compact domain of a spin manifold. The main tool is to solve some boundary problems for the Dirac operator of the domain under boundary conditions of Atiyah-Patodi-Singer type. Spinorial techniques are used to give simple proofs of classical results for compact embedded hypersurfaces.
متن کاملA Remark on Zhong-yangs Eigenvalue Estimate
Moreover we know exactly when the equality holds: if and only if D is a disc. For any optimal geometric inequality it is important to have a complete understanding of the equality case. Sometimes this can be easily achieved by checking the proof of the inequality. Take as an example the following elegant theorem due to Lichenerowicz [L]: let (M; g) be a compact Riemannian manifold of dimension ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Differential Geometry and its Applications
سال: 2008
ISSN: 0926-2245
DOI: 10.1016/j.difgeo.2007.11.019