# CSASC 2013

9-13 June 2013
Koper, Slovenia
UTC timezone
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# DIFFERENTIAL EQUATIONS IN COMPLEX DOMAIN AND SPHERICAL REAL HYPERSURFACES

Presented by Dr. Ilya KOSSOVSKIY
Type: Oral presentation
Track: General Session

## Content

We use a remarkable connection between real hypersurfaces in complex space and second-order differential equations in complex domains for the study of nonminimal real hypersurfaces in complex affine 2-space. We find necessary and sufficient conditions for a local CR-mapping at a Levi nondegenerate point into a sphere (if the latter exists) to extend holomorphically to the complex locus. As an application, we prove the bound $dim aut(M,0) \leq 5$ for the infinitesimal automorphism algebra of an arbitrary nonminimal at the origin Levi-nonflat hypersurface in $C^2$. This work is joint with R.Shafikov.

## Place

Location: Koper, Slovenia

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