Fully Nonlinear Elliptic Equations with Gradient Terms on Hermitian Manifolds
Bo Guan, Xiaolan Nie
Abstract
Abstract We derive a priori 2nd-order estimates for fully nonlinear elliptic equations that depend on the gradients of solutions on compact Hermitian manifolds, which is a crucial step in solving the equations. We introduce the concept of rank of the tangent cones at infinity to level hypersurfaces of the defining function of the equation to overcome difficulties caused by presence of the gradient terms. We were motivated by the fact that there had been increasing interests in fully nonlinear PDEs from complex geometry and aimed to develop general methods to cover a wide class of equations.
Topics & Concepts
MathematicsNonlinear systemHermitian matrixA priori and a posterioriTangentTangent coneRank (graph theory)InfinityCover (algebra)Mathematical analysisFunction (biology)Applied mathematicsPure mathematicsGeometryEvolutionary biologyMechanical engineeringPhilosophyBiologyPhysicsCombinatoricsEpistemologyQuantum mechanicsEngineeringGeometry and complex manifoldsGeometric Analysis and Curvature FlowsAlgebraic Geometry and Number Theory