The maximum principle for hypersurfaces with vanishing curvature functions

Homaloidal hypersurfaces and hypersurfaces with vanishing Hessian

We introduce various families of irreducible homaloidal hypersurfaces in projective space Pr, for all r ≥ 3. Some of these are families of homaloidal hypersurfaces whose degrees are arbitrarily large as compared to the dimension of the ambient projective space. The existence of such a family solves a question that has naturally arisen from the consideration of the classes of homaloidal hypersur...

On the Maximum Principle for Harmonic Functions

Some generalizations of the maximum principle for harmonic functions are discussed. §

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

Cylindrical Estimates for Hypersurfaces Moving by Convex Curvature Functions

Convexity estimates for hypersurfaces moving by convex curvature functions

We consider the evolution of compact hypersurfaces by fully non-linear, parabolic curvature ows for which the normal speed is given by a smooth, convex, degree one homogeneous function of the principal curvatures. We prove that solution hypersurfaces on which the speed is initially positive become weakly convex at a singularity of the ow. The result extends the convexity estimate [HS99b] of Hui...