The Levi Monge-Ampère equation: Smooth regularity of strictly Levi convex solutions

Content Provider	Semantic Scholar
Author	Montanari, Annamaria Lascialfari, Francesca
Copyright Year	2004
Abstract	We prove smoothness of strictly Levi convex solutions to the Levi equation in several complex variables. This equation is fully non linear and naturally arises in the study of real hypersurfaces in ℂn+1, for n ≥ 2. For a particular choice of the right-hand side, our equation has the meaning of total Levi curvature of a real hypersurface ℂn+1 and it is the analogous of the equation with prescribed Gauss curvature for the complex structure. However, it is degenerate elliptic also if restricted to strictly Levi convex functions. This basic failure does not allow us to use elliptic techniques such in the classical real and complex Monge-Ampère equations. By taking into account the natural geometry of the problem we prove that first order intrinsic derivatives of strictly Levi convex solutions satisfy a good equation. The smoothness of solutions is then achieved by mean of a bootstrap argument in tangent directions to the hypersurface.
Starting Page	331
Ending Page	353
Page Count	23
File Format	PDF HTM / HTML
DOI	10.1007/BF02922076
Alternate Webpage(s)	http://www.dm.unibo.it/~montanar/HTML/montanar.pdf
Alternate Webpage(s)	https://doi.org/10.1007/BF02922076
Volume Number	14
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article