Hessian equations of Krylov type on compact Hermitian manifolds
In this article, we are concerned with the equations of Krylov type on compact Hermitian manifolds, which are in the form of the linear combinations of the elementary symmetric functions of a Hermitian matrix. Under the assumption of the 𝒞-subsolution, we obtain a priori estimates in Γk−1{\Gamma }_{...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2022-10-01
|
| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2022-0504 |
| _version_ | 1811324143146106880 |
|---|---|
| author | Zhou Jundong Chu Yawei |
| author_facet | Zhou Jundong Chu Yawei |
| author_sort | Zhou Jundong |
| collection | DOAJ |
| description | In this article, we are concerned with the equations of Krylov type on compact Hermitian manifolds, which are in the form of the linear combinations of the elementary symmetric functions of a Hermitian matrix. Under the assumption of the 𝒞-subsolution, we obtain a priori estimates in Γk−1{\Gamma }_{k-1} cone. By using the method of continuity, we prove an existence theorem, which generalizes the relevant results. As an application, we give an alternative way to solve the deformed Hermitian Yang-Mills equation on compact Kähler threefold. |
| first_indexed | 2024-04-13T14:09:06Z |
| format | Article |
| id | doaj.art-a6cab68468ca4100b8ee72705b74b0fc |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-04-13T14:09:06Z |
| publishDate | 2022-10-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-a6cab68468ca4100b8ee72705b74b0fc2022-12-22T02:43:50ZengDe GruyterOpen Mathematics2391-54552022-10-012011126114410.1515/math-2022-0504Hessian equations of Krylov type on compact Hermitian manifoldsZhou Jundong0Chu Yawei1School of Mathematics and Statistics, Fuyang Normal University, Fuyang 236037, Anhui, P.R. ChinaSchool of Mathematics and Statistics, Fuyang Normal University, Fuyang 236037, Anhui, P.R. ChinaIn this article, we are concerned with the equations of Krylov type on compact Hermitian manifolds, which are in the form of the linear combinations of the elementary symmetric functions of a Hermitian matrix. Under the assumption of the 𝒞-subsolution, we obtain a priori estimates in Γk−1{\Gamma }_{k-1} cone. By using the method of continuity, we prove an existence theorem, which generalizes the relevant results. As an application, we give an alternative way to solve the deformed Hermitian Yang-Mills equation on compact Kähler threefold.https://doi.org/10.1515/math-2022-0504hessian equationshermitian manifoldssubsolution condition35j6035b4553c55 |
| spellingShingle | Zhou Jundong Chu Yawei Hessian equations of Krylov type on compact Hermitian manifolds Open Mathematics hessian equations hermitian manifolds subsolution condition 35j60 35b45 53c55 |
| title | Hessian equations of Krylov type on compact Hermitian manifolds |
| title_full | Hessian equations of Krylov type on compact Hermitian manifolds |
| title_fullStr | Hessian equations of Krylov type on compact Hermitian manifolds |
| title_full_unstemmed | Hessian equations of Krylov type on compact Hermitian manifolds |
| title_short | Hessian equations of Krylov type on compact Hermitian manifolds |
| title_sort | hessian equations of krylov type on compact hermitian manifolds |
| topic | hessian equations hermitian manifolds subsolution condition 35j60 35b45 53c55 |
| url | https://doi.org/10.1515/math-2022-0504 |
| work_keys_str_mv | AT zhoujundong hessianequationsofkrylovtypeoncompacthermitianmanifolds AT chuyawei hessianequationsofkrylovtypeoncompacthermitianmanifolds |