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A comparison theorem for the first Dirichlet eigenvalue of a domain in a Kaehler submanifold
Fernando GiménezVicente MiquelFrancisco J. Carrerassubject
GeodesicMathematics::Complex VariablesMathematical analysisHolomorphic functionGeneral MedicineKähler manifoldMathematics::Spectral TheorySubmanifoldCurvaturesymbols.namesakeDirichlet eigenvaluesymbolsDirichlet's theorem on arithmetic progressionsMathematics::Differential GeometrySectional curvatureMathematics::Symplectic GeometryMathematicsdescription
AbstractWe give a sharp lower bound for the first eigenvalue of the Dirichlet eigenvalue problem on a domain of a complex submanifold of a Kaehler manifold with curvature bounded from above. The bound on the first eigenvalue is given as a function of the extrinsic outer radius and the bounds on the curvature, and it is attained only on geodesic spheres of a space of constant holomorphic sectional curvature embedded in the Kaehler manifold as a totally geodesic submanifold.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1994-04-01 | Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics |