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Bo Guan

Publications and source records attributed to Bo Guan.

23 records · Page 2Linked to original sources
arXiv2009

Complex Monge-Ampere equations and totally real submanifolds

We study the Dirichlet problem for complex Monge-Ampere equations in Hermitian manifolds with general (non-pseudoconvex) boundary. Our main result extends the classical theorem of Caffarelli, Kohn, Nirenberg and Spruck in the flat case. We also consider the equation on compact manifolds without boundary, attempting to generalize Yau's theorems in the Kaehler case. As applications of the main result we study some connections between the homogeneous complex Monge-Ampere ({\em HCMA}) equation and totally real submanifolds, and a special Dirichlet problem for the HCMA equation related to Donaldson's conjecture on geodesics in the space of Kaehler metrics.

math.DG↗
arXiv2009

Complex Monge-Ampere equations on Hermitian manifolds

We study complex Monge-Ampere equations on Hermitian manifolds, extending classical existence results of Yau and Aubin in the Kahler case, and those of Caffarelli, Kohn, Nirenberg and Spruck for the Dirichlet problem in $C^n$. As an application we generalize existing results on the Donaldson conjecture on geodesics in the space of Kahler metrics to the Hermitian setting.

math.DG↗
arXiv2008

Hypersurfaces of Constant Curvature in Hyperbolic Space II

We find complete hypersurfaces of constant curvature in hyperbolic space with a prescribed asymptotic boundary at infinity for a general class of (elliptic) curvature functions which includes the higher order mean curvatures and their curvature quotients.

math.DG↗