$C^{1,1}$ regularity of geodesics in the space of volume forms

Abstract

We prove a $C^{1,1}$ estimate for solutions of a class of fully nonlinear equations introduced by Chen-He. As an application, we prove the $C^{1,1}$ regularity of geodesics in the space of volume forms.

7 pages; v2 some more details added, typos corrected