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Foliations by complex manifolds involving the complex Hessian

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Ławrynowicz J., Kalina J., Okada M.

Instytut Matematyczny Polskiej Akademii Nauk

CONTENTS Summary...................................................................................................................................................................3 1. Introduction and an outline of results....................................................................................................................5 2. Capacities on complex manifolds and the generalized complex Monge-Ampère equations..................................8 3. Foliations............................................................................................................................................................10 4. Proof of the existence theorem in the holomorphically decomposable case.......................................................12 5. Proof of the existence theorem in the exterior product case...............................................................................14 6. Natural Markov processes connected with the foliation $ℒ_{k+p-1}$.................................................................16 7. Properties of canonical diffusions.......................................................................................................................18 8. Laplace-Beltrami operator on Riemannian manifolds.........................................................................................21 9. Harmonic theory on compact complex manifolds................................................................................................23 10. Laplace-Beltrami operator as the generator of a canonical diffusion................................................................27 11. Laplace-Beltrami operator in the case of the sphere and the hyperboloid........................................................29 12. Complex Hessian involving convex functions....................................................................................................33 13. Some examples of applications.........................................................................................................................36 14. Hypersurfaces in ℂ³ depending on two holomorphic functions.........................................................................41 References.............................................................................................................................................................43

Ograniczanie wyników

1 Kalina J.

1 Okada M.

1 Ławrynowicz J.

1 1994

Wyniki wyszukiwania

Foliations by complex manifolds involving the complex Hessian