Abstract: We derive global curvature estimates for closed strictly starshaped (n-2)-convex hypersurfaces in warped product manifolds, satisfying the prescribed (n-2)-curvature equation with a general right-hand side. The proof is inspired by the recent breakthrough of [Guan-Ren-Wang CPAM 2015] and it can be readily adapted to establish curvature estimates for semi-convex and (k+1)-convex solutions to the general k-curvature equations; it can also be used to prove the same estimates for prescribed curvature measure type equations. If time permits, we may also discuss the estimates for another class of Hessian type equations.

Brief Bio: Bin Wang is currently a second-year PhD student at the Chinese University of Hong Kong, studying under the supervision of Man-Chun Lee. At this moment, he is interested in fully nonlinear PDEs in geometry.

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