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Integral formulas for a class of curvature PDE's and applications to isoperimetric inequalities and to symmetry problems
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Vittorio Martino
Veröffentlicht/Copyright:
8. Februar 2010
Abstract
We prove integral formulas for closed hypersurfaces in ℂn+1, which furnish a relation between elementary symmetric functions in the eigenvalues of the complex Hessian matrix of the defining function and the Levi curvatures of the hypersurface. Then we follow the Reilly approach to prove an isoperimetric inequality. As an application, we obtain the “Soap Bubble Theorem” for star-shaped domains with positive and constant Levi curvatures bounding the classical mean curvature from above.
Received: 2007-07-16
Revised: 2008-05-05
Published Online: 2010-02-08
Published in Print: 2010-March
© de Gruyter 2010
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Artikel in diesem Heft
- Lp estimates for parabolic magnetic Schrödinger operators
- Calculation of UNil for the cyclic group of order two
- Lie theoretic significance of the measure topologies associated with a finite trace
- Integral formulas for a class of curvature PDE's and applications to isoperimetric inequalities and to symmetry problems
- The finiteness of NK1(ℤ[G])
- Poincaré duality pairs of dimension three
- Optimal quantization of probabilities concentrated on small balls
- A sharp diameter bound for unipotent groups of classical type over ℤ/pℤ
- Homological localizations of Eilenberg–MacLane spectra
- A∞-coalgebra structure maps that vanish on H∗(K(π, n); ℤp)
- The cohomology groups of the outer Whitehead automorphism group of a free product
- Dual topology of the motion groups
Artikel in diesem Heft
- Lp estimates for parabolic magnetic Schrödinger operators
- Calculation of UNil for the cyclic group of order two
- Lie theoretic significance of the measure topologies associated with a finite trace
- Integral formulas for a class of curvature PDE's and applications to isoperimetric inequalities and to symmetry problems
- The finiteness of NK1(ℤ[G])
- Poincaré duality pairs of dimension three
- Optimal quantization of probabilities concentrated on small balls
- A sharp diameter bound for unipotent groups of classical type over ℤ/pℤ
- Homological localizations of Eilenberg–MacLane spectra
- A∞-coalgebra structure maps that vanish on H∗(K(π, n); ℤp)
- The cohomology groups of the outer Whitehead automorphism group of a free product
- Dual topology of the motion groups
