We introduce certain energy functionals to complex Monge–Ampère equations over bounded domains with inhomogeneous boundary conditions, and use these functionals to show the convergence of solutions to certain parabolic Monge–Ampère equations.
Using equivariant cohomology, we construct a family of holomorphic invariants which include the famous Futaki invariant and its generalization to singular variety as special cases. We are also using this viewpoint to compute the generalized Futaki invariant for complete intersections.
Abstract. In this paper, integrals involving both real and complex Hessian operators over bounded domains are studied. Poincaré type inequalities are proved in both cases, which generalizes an early result of Trudinger and Wang.
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