Hölder regularity of \(\overline{\partial_ b}\) in convex-concave hypersurfaces
type: Item
instance of: scholarly article
title: Hölder regularity of \(\overline{\partial_ b}\) in convex-concave hypersurfaces
zbMATH Open document ID: 0843.32008
DOI: 10.1007/PL00004523
published in: Mathematische Zeitschrift
publication date: 1996-03-21T00:00:00Z
full work available at URL: https://eudml.org/doc/174867
review text: Let \(M\) be a real hypersurface of class \(C^2\) in a complex analytic manifold. Suppose that the Levi form of \(M\) has at each point at least a pair of eigenvalues of opposite sign. In this paper we prove a regularity theorem for \(\overline {\partial}_b\) and a theorem of type Hartogs-Bochner on \(M\). Our key ingredient is a Hölder estimate for a local Martinelli-Bochner kernel constructed by \textit{B. Fischer} and \textit{J. Leiterer} on \(M\) [Math. Z. 214, No. 4, 659-681 (1993; Zbl 0791.32006)].
Mathematics Subject Classification ID: 32F10
Mathematics Subject Classification ID: 32W05
Mathematics Subject Classification ID: 32A25
Mathematics Subject Classification ID: 32D15
Mathematics Subject Classification ID: 32V40
zbMATH DE Number: 838482
zbMATH Keywords: 1-convex
zbMATH Keywords: 1-concave
zbMATH Keywords: real hypersurface
zbMATH Keywords: Levi form
zbMATH Keywords: regularity
zbMATH Keywords: \(\overline {\partial}_ b\)
zbMATH Keywords: Hölder estimate
author: Moulay Youssef Barkatou
MaRDI profile type: Publication
OpenAlex ID: W2045779686
description: scientific article; zbMATH DE number 838482