Hölder regularity of generic manifold

2016/02/05 by Azimbay Sadullaev, Sadullaev, Azimbay, Ahmed Zeriahi +1
Mathematics · #32E30 #32U05 #32U15 #32U35 #32V40 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:32E30 #msc:32U05 #msc:32U15 #msc:32U35 #msc:32V40

paper · pdf · doi:10.48550/arxiv.1602.01964

To appear in Ann. Scuola Norm. Sup. Pisa Cl. Sci. in 2016; 14 pages

arxiv created 2016/02/05 · arxiv updated 2016/02/08

Abstract

In this paper we study Hölder continuity of the pluricomplex Green function with logarithmic growth at infinity of a smooth generic submanifold of \Cⁿ. In particular we prove that the pluricomplex Green function of any C²-smooth generic compact submanifold of \Cⁿ (without boundary) is Lipschitz continuous in \Cⁿ.

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