An interior estimate for convex solutions and a rigidity theorem
By Ming Li, Changyu Ren, Zhizhang Wang. 2015
96 citations recorded by the source corpus.
We establish an interior $C^2$ estimate for $k+1$ convex solutions to Dirichlet problems of $k$-Hessian equations. We also use such estimate to obtain a rigidity theorem for $k+1$ convex entire solutions of $k$-Hessian equations in Euclidean space.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/7c174e3a71922e3080de8b66ce616ac0549e9aa8
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In Applied Mathematics
- Sebastien Picard
- Duong H. Phong
- Xiangwen Zhang
- Zhizhang Wang
- Changyu Ren
- B. Weinkove
- Valentino Tosatti
- G'abor Sz'ekelyhidi
In Geometry and Topology
- Zhizhang Wang
- Changyu Ren
- Duong H. Phong
- Xiangwen Zhang
- Sebastien Picard
- B. Weinkove
- Valentino Tosatti
- G'abor Sz'ekelyhidi
Citations in the corpus
- On the curvature estimates for Hessian equations (2016, background): “More reference about these type of estimates can be found in [13, 30].”
- The global curvature estimate for the n-2 Hessian equation (2020, methodology): “Based on Lemma 36, an induction argument being similar to the proof of Corollary 10 in [31] can be applied here.”
- A second order estimate for general complex Hessian equations (2015, methodology): “2015], used also in [Li et al. 2016], is to extract a good term involving |D1g1̄1| 2 from A1.”