On the behavior of strictly plurisubharmonic functions near real hypersurfaces

Abstract

We describe the behavior of certain strictly plurisubharmonic functions near some real hypersurfaces in ℂⁿ, n≥3. Given a hypersurface we study continuous plurisubharmonic functions which are zero on the hypersurface and have Monge–Ampère mass greater than one in a one-sided neighborhood of the hypersurface. If we can find complex curves which have sufficiently high contact order with the hypersurface then the plurisubharmonic functions we study cannot be globally Lipschitz in the one-sided neighborhood.