11 citations · 48 across the 15 of their papers we have counts for
15 papers
Banach-Mazur Distance from to
Longzhen Zhang, Lingxu Meng, Senlin Wu
The maximum of the Banach-Mazur distance , where ranges over the set of all -dimensional real Banach spaces, is difficult to compute. In fact, it…
Holomorphic Koszul-Brylinski homology via Dolbeault cohomology
Lingxu Meng
We use the Dolbeault cohomology to investigate the Koszul-Brylinski homology on holomorphic Poisson manifolds. We obtain the Leray-Hirsch theorem for Hochschild homology and the Ma…
Covering functionals of convex polytopes with few vertices
Xia Li, Lingxu Meng, Senlin Wu
By using elementary yet interesting observations and refining techniques used in a recent work by Fei Xue et al., we present new upper bounds for covering functionals of convex pol…
Blow-up formulae for twisted cohomologies with supports
Lingxu Meng
We study twisted cohomologies with paracompactifying families of supports. The Kunneth theorems, Leray-Hirsch theorems and self-intersection formulae are established. Based on thes…
Spin Solitons in Spin-1 Bose-Einstein Condensates
Ling-Zheng Meng, Yan-Hong Qin, Li-Chen Zhao
Solitons in multi-component Bose-Einstein condensates have been paid much attention, due to the stability and wide applications of them. The exact soliton solutions are usually obt…
Hypercohomologies of truncated twisted holomorphic de Rham complexes
Lingxu Meng
We investigate the hypercohomologies of truncated twisted holomorphic de Rham complexes on (not necessarily compact) complex manifolds. In particular, we generalize Leray-Hirsch, K…
Algebraic cycles on fiber bundles of Leray-Hirsch type
Lingxu Meng
We give a theorem of Leray-Hirsch type for Chow groups and use it to study the Hogde and Grothendieck's standard conjectures for algebraic fiber bundles of Leray-Hirsch type. Morev…
The heredity and bimeromorphic invariance of the -lemma property
Lingxu Meng
We give a simple proof of a result on the -lemma property under a blow-up transformation by Deligne--Griffiths--Morgan--Sullivan's criterion. Here, we use a…
Mayer-Vietoris systems and their applications
Lingxu Meng
We introduce notions such as cdp presheaf, cds precosheaf, Mayer-Vietoris system, and investigate their properties. As applications, we study cohomologies with values in local syst…
Complex Balanced Spaces
Jixiang Fu, Lingxu Meng, Wei Xia
In this paper, the concept of balanced manifolds is generalized to reduced complex spaces: the class B and balanced spaces. Compared with the case of Kahlerian, the class B is simi…
Morse-Novikov cohomology on complex manifolds
Lingxu Meng
We view Dolbeault-Morse-Novikov cohomology H^{p,q}_η(X) as the cohomology of the sheaf Ω_{X,η}^p of η-holomorphic p-forms and give several bimeromorphic invariants. Analogue to Dol…
Leray-Hirsch theorem and blow-up formula for Dolbeault cohomology
Lingxu Meng
We prove a theorem of Leray-Hirsch type and give an explicit blow-up formula for Dolbeault cohomology on (\emph{not necessarily compact}) complex manifolds. We give applications to…
Morse-Novikov cohomology for blow-ups of complex manifolds
Lingxu Meng
The weight -sheaf helps us to reinterpret Morse-Novikov cohomologies via sheaf theory. We give several theorems of Künneth and Leray-Hirsch types.…
Strongly Gauduchon spaces
Lingxu Meng, Wei Xia
We define strongly Gauduchon spaces and the class SG which are generalization of strongly Gauduchon manifolds in complex spaces. Comparing with the case of Kahlerian, the strongly…
Holomorphic Gromov's partial order
Lingxu Meng
As in [5], we study holomorphic maps of positive degree between compact complex manifolds, and prove that any holomorphic map of degree one from a compact complex manifold to itsel…