Second order estimates for Hessian type fully nonlinear elliptic equations on Riemannian manifolds
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We derive a priori estimates for second order derivatives of solutions to a wide class of fully nonlinear elliptic equations on Riemannian manifolds. There had been significant work in this direction, especially in connection with important geometric problems and other applications, but one had to make use of the special structures or needed extra assumptions which are more technical in nature to overcome various difficulties. In this paper we are able to remove most of the technical assumptions and derive the estimates under conditions which are close to optimal. These estimates enable one to prove existence results which are new even for bounded domains in Euclidean space.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/9c417b4abe1b56e426adea02c29e0b5779ebc392
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In Applied Mathematics
- G'abor Sz'ekelyhidi
- Valentino Tosatti
- B. Weinkove
- Duong H. Phong
- Xiaokui Yang
- Jian Song
- Dat T. To
- V. Datar
In Geometry and Topology
- G'abor Sz'ekelyhidi
- Valentino Tosatti
- B. Weinkove
- Duong H. Phong
- Xiaokui Yang
- Jian Song
- Dat T. To
- Jianchun Chu
Citations in the corpus
- Gauduchon metrics with prescribed volume form (2015, background): “bharmonic functions, and [8, 20] for the standard K¨ahler case where ω= α+ √ −1∂∂u. (7) The complex setting is very different from the real analogue of (1.7), treated for example in more generality in [16]. The underlying reason is the two different types of complex derivatives. In our case the specia”