A priori Estimates and Existence for a Class of Fully Nonlinear Elliptic Equations in Conformal Geometry*
By Xu-jia Wang. 2006
69 citations recorded by the source corpus.
In this paper we prove the interior gradient and second derivative estimates for a class of fully nonlinear elliptic equations determined by symmetric functions of eigenvalues of the Ricci or Schouten tensors. As an application we prove the existence of solutions to the equations when the manifold is locally conformally flat or the Ricci curvature is positive.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/1c445293002cde7825da21a0b701a37d356b7ecf
How researchers see this paper
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In Applied Mathematics
- Bo Guan
- Luc Nguyen
- Yanyan Li
- Valentino Tosatti
- Jingang Xiong
- Tianling Jin
- Pengfei Guan
- Luis Caffarelli
In Geometry and Topology
- Luc Nguyen
- Bo Guan
- Yanyan Li
- Valentino Tosatti
- B. Weinkove
- Pengfei Guan
- Xinan Ma
- G'abor Sz'ekelyhidi
Citations in the corpus
- A compactness theorem for a fully nonlinear Yamabe problem under a lower Ricci curvature bound (2012, methodology): “For this step in the case μ+Γ ≤ 1, we make use of Bishop’s comparison theorem, a Riemannian version of Hawking’s singularity theorem in relativity, a Liouville theorem in [27] and local gradient estimates for solutions of (6) ([20, 13, 29, 45]).”
- Complete Conformal Metrics of Negative Ricci Curvature on Compact Manifolds with Boundary (2008, background): “Their result has been extended to more general symmetric functions; see for instance [5], [12], [20], [19] and [28].”
- Local gradient estimates of solutions to some conformally invariant fully nonlinear equations (2006, methodology): “It has been observed independently by Wang in [38] that Theorem 1.”