TY - JOUR
T1 - Regularity of degenerate k-Hessian equations on closed Hermitian manifolds
AU - Zhang, Dekai
N1 - Publisher Copyright:
© 2022 Dekai Zhang, published by De Gruyter.
PY - 2022/1/1
Y1 - 2022/1/1
N2 - In this article, we are concerned with the existence of weak C 1, 1 solution of the k k-Hessian equation on a closed Hermitian manifold under the optimal assumption of the function in the right-hand side of the equation. The key points are to show the weak C 1, 1 estimates. We prove a Cherrier-Type inequality to obtain the C 0 estimate, and the complex Hessian estimate is proved by using an auxiliary function, which was motivated by Hou et al. and Tosatti and Weinkove. Our result generalizes the Kähler case proved by Dinew et al.
AB - In this article, we are concerned with the existence of weak C 1, 1 solution of the k k-Hessian equation on a closed Hermitian manifold under the optimal assumption of the function in the right-hand side of the equation. The key points are to show the weak C 1, 1 estimates. We prove a Cherrier-Type inequality to obtain the C 0 estimate, and the complex Hessian estimate is proved by using an auxiliary function, which was motivated by Hou et al. and Tosatti and Weinkove. Our result generalizes the Kähler case proved by Dinew et al.
KW - Hermitian manifold
KW - degenerate k-Hessian equations
KW - optimal regularity
UR - https://www.scopus.com/pages/publications/85140291518
U2 - 10.1515/ans-2022-0025
DO - 10.1515/ans-2022-0025
M3 - 文章
AN - SCOPUS:85140291518
SN - 1536-1365
VL - 22
SP - 534
EP - 547
JO - Advanced Nonlinear Studies
JF - Advanced Nonlinear Studies
IS - 1
ER -