In this paper,we consider the deformed Hermitian-Yang-Mills equation on closed almost Hermitian manifolds.In the case of the hypercritical phase,we derive a priori estimates under the existence of an admissible C-subs...In this paper,we consider the deformed Hermitian-Yang-Mills equation on closed almost Hermitian manifolds.In the case of the hypercritical phase,we derive a priori estimates under the existence of an admissible C-subsolution.As an application,we prove the existence of solutions for the deformed Hermitian-Yang-Mills equation under the condition of existence of a supersolution.展开更多
In this paper,we analyze the asymptotic behaviour of the Hermitian-Yang-Mills flow over a compact non-Kahler manifold(X,g)with the Hermitian metric g satisfying the Gauduchon and Astheno-Kahler condition.
In this paper,we study the curvature estimate of the Hermitian–Yang–Mills flow on holomorphic vector bundles.In one simple case,we show that the curvature of the evolved Hermitian metric is uniformly bounded away fr...In this paper,we study the curvature estimate of the Hermitian–Yang–Mills flow on holomorphic vector bundles.In one simple case,we show that the curvature of the evolved Hermitian metric is uniformly bounded away from the analytic subvariety determined by the Harder–Narasimhan–Seshadri filtration of the holomorphic vector bundle.展开更多
The non-abelian Hodge correspondence was established by Corlette(1988),Donaldson(1987),Hit chin(1987)and Simpson(1988,1992).It states that on a compact Kahler manifold(X,ω),there is a one-to-one correspondence betwee...The non-abelian Hodge correspondence was established by Corlette(1988),Donaldson(1987),Hit chin(1987)and Simpson(1988,1992).It states that on a compact Kahler manifold(X,ω),there is a one-to-one correspondence between the moduli space of semi-simple flat complex vector bundles and the moduli space of poly-stable Higgs bundles with vanishing Chern numbers.In this paper,we extend this correspondence to the projectively flat bundles over some non-Kahler manifold cases.Firstly,we prove an existence theorem of Poisson metrics on simple projectively flat bundles over compact Hermitian manifolds.As its application,we obtain a vanishing theorem of characteristic classes of projectively flat bundles.Secondly,on compact Hermitian manifolds which satisfy Gauduchon and astheno-K?hler conditions,we combine the continuity method and the heat flow method to prove that every semi-stable Higgs bundle withΔ(E,?E)·[ωn-2]=0 must be an extension of stable Higgs bundles.Using the above results,over some compact non-Kahler manifolds(M,ω),we establish an equivalence of categories between the category of semi-stable(poly-stable)Higgs bundles(E,?E,φ)withΔ(E,?E)·[ωn-2]=0 and the category of(semi-simple)projectively flat bundles(E,D)with(-1)(1/2)FD=α■IdE for some real(1,1)-formα.展开更多
基金supported by the project“Analysis and Geometry on Bundle”of Ministry of Science and Technology of the People’s Republic of China(Grant No.SQ2020YFA070080)National Natural Science Foundation of China(Grant Nos.11625106,11571332 and 11721101)。
文摘In this paper,we consider the deformed Hermitian-Yang-Mills equation on closed almost Hermitian manifolds.In the case of the hypercritical phase,we derive a priori estimates under the existence of an admissible C-subsolution.As an application,we prove the existence of solutions for the deformed Hermitian-Yang-Mills equation under the condition of existence of a supersolution.
基金supported by National Natural Science Foundation of China(Grant No.11131007)。
文摘In this paper,we analyze the asymptotic behaviour of the Hermitian-Yang-Mills flow over a compact non-Kahler manifold(X,g)with the Hermitian metric g satisfying the Gauduchon and Astheno-Kahler condition.
基金supported in part by NSF in China,Nos.11625106,11571332,and 11721101.
文摘In this paper,we study the curvature estimate of the Hermitian–Yang–Mills flow on holomorphic vector bundles.In one simple case,we show that the curvature of the evolved Hermitian metric is uniformly bounded away from the analytic subvariety determined by the Harder–Narasimhan–Seshadri filtration of the holomorphic vector bundle.
基金supported by the National Key R&D Program of China(Grant No.2020YFA0713100)National Natural Science Foundation of China(Grant Nos.12141104,11801535,11721101and 11625106)。
文摘The non-abelian Hodge correspondence was established by Corlette(1988),Donaldson(1987),Hit chin(1987)and Simpson(1988,1992).It states that on a compact Kahler manifold(X,ω),there is a one-to-one correspondence between the moduli space of semi-simple flat complex vector bundles and the moduli space of poly-stable Higgs bundles with vanishing Chern numbers.In this paper,we extend this correspondence to the projectively flat bundles over some non-Kahler manifold cases.Firstly,we prove an existence theorem of Poisson metrics on simple projectively flat bundles over compact Hermitian manifolds.As its application,we obtain a vanishing theorem of characteristic classes of projectively flat bundles.Secondly,on compact Hermitian manifolds which satisfy Gauduchon and astheno-K?hler conditions,we combine the continuity method and the heat flow method to prove that every semi-stable Higgs bundle withΔ(E,?E)·[ωn-2]=0 must be an extension of stable Higgs bundles.Using the above results,over some compact non-Kahler manifolds(M,ω),we establish an equivalence of categories between the category of semi-stable(poly-stable)Higgs bundles(E,?E,φ)withΔ(E,?E)·[ωn-2]=0 and the category of(semi-simple)projectively flat bundles(E,D)with(-1)(1/2)FD=α■IdE for some real(1,1)-formα.
