The Sobolev inequality for complex Hessian equations

Bin Zhou

doi:10.1007/s00209-012-1084-y

The Sobolev inequality for complex Hessian equations

Bin Zhou^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

In this paper, we study the complex Hessian equations by an gradient flow method. We prove a Sobolev inequality for k-plurisubharmonic functions analogous to that for real Hessian equations (Wang in Indiana Univ Math J 43:25-54, 1994; Lecture Notes in Mathematics, vol. 1977, 2009).

Original language	English
Pages (from-to)	531-549
Number of pages	19
Journal	Mathematische Zeitschrift
Volume	274
Issue number	1-2
DOIs	https://doi.org/10.1007/s00209-012-1084-y
Publication status	Published - Jun 2013
Externally published	Yes

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10.1007/s00209-012-1084-y

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AB - In this paper, we study the complex Hessian equations by an gradient flow method. We prove a Sobolev inequality for k-plurisubharmonic functions analogous to that for real Hessian equations (Wang in Indiana Univ Math J 43:25-54, 1994; Lecture Notes in Mathematics, vol. 1977, 2009).

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JO - Mathematische Zeitschrift

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The Sobolev inequality for complex Hessian equations

Abstract

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