Fully non-linear elliptic equations on compact Hermitian manifolds
By G'abor Sz'ekelyhidi. Journal of differential geometry, 2015
206 citations recorded by the source corpus.
We derive a priori estimates for solutions of a general class of fully non-linear equations on compact Hermitian manifolds. Our method is based on ideas that have been used for different specific equations, such as the complex Monge-Ampere, Hessian and inverse Hessian equations. As an application we solve a class of Hessian quotient equations on Kahler manifolds assuming the existence of a suitable subsolution. The method also applies to analogous equations on compact Riemannian manifolds.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/e33ed271e5ffedf832fd64b6891cdd49e1f171e9
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In Applied Mathematics
- Dat T. To
- Jian Song
- Duong H. Phong
- V. Datar
- Vamsi Pingali
- G'abor Sz'ekelyhidi
- Valentino Tosatti
- B. Weinkove
In Geometry and Topology
- Dat T. To
- Jian Song
- Duong H. Phong
- V. Datar
- Vamsi Pingali
- G'abor Sz'ekelyhidi
- Valentino Tosatti
- B. Weinkove
Citations in the corpus
- Fully non-linear parabolic equations on compact Hermitian manifolds (2017, methodology): “In particular, they show that their notions, called C-subsolution in [50], do imply the existence of solutions and estimates for a wide variety of fully non-linear elliptic equations on Hermitian manifolds.”
- A numerical criterion for generalised Monge-Ampère equations on projective manifolds (2020, methodology): “1 immediately implies Conjecture 23 of Székelyhidi [38] (which itself generalises a conjecture of LejmiSzékelyhidi [26]) for the inverse Hessian equations in the projective case.”
- Nakai-Moishezon criterions for complex Hessian equations (2020, background): “4) is later interpreted in [21] as a subsolution of the J-equation.”