Curvature estimates for minimal hypersurfaces in singular spaces

We here prove pointwise curvature estimates for minimal hypersurfaces in singular spaces, using the integral curvature estimate and a generalized Simons inequality which were established recently. A further basic ingredient is a new Sobolev type inequality for stationary hypersurfaces.Oblatum 19-IX-1994This research was supported by the Deutsche Forschungsgemeinschaft through a Heisenberg award. Part of the work described here was carried out during visits to Dipartimento Matematica Applicata, University of Firenze and Department of Mathematics, Stanford University. The author would like to express his gratitude to both institutions for their kind hospitality and support. Also it is a pleasure to thank the referee for his useful comments concerning the formulation of the main theorem.