scholarly journals A Stampacchia-type inequality for a fourth-order elliptic operator on Kähler manifolds and applications

2010 ◽  
pp. 159-173 ◽  
Author(s):  
Luca Lussardi
Keyword(s):  
Elliptic Operator ◽  
Fourth Order ◽  
Type Inequality ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Order Elliptic Operator

scholarly journals Chern Class Inequalities on Polarized Manifolds and Nef Vector Bundles

2020 ◽  
Author(s):  
Ping Li ◽  
Fangyang Zheng
Keyword(s):  
Chern Class ◽  
Vector Bundles ◽  
Euler Number ◽  
Type Inequality ◽  
Chern Number ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Bisectional Curvature ◽  
Chern Numbers ◽  
Nef Vector Bundles

Abstract This article is concerned with Chern class and Chern number inequalities on polarized manifolds and nef vector bundles. For a polarized pair $(M,L)$ with $L$ very ample, our 1st main result is a family of sharp Chern class inequalities. Among them the 1st one is a variant of a classical result and the equality case of the 2nd one is a characterization of hypersurfaces. The 2nd main result is a Chern number inequality on it, which includes a reverse Miyaoka–Yau-type inequality. The 3rd main result is that the Chern numbers of a nef vector bundle over a compact Kähler manifold are bounded below by the Euler number. As an application, we classify compact Kähler manifolds with nonnegative bisectional curvature whose Chern numbers are all positive. A conjecture related to the Euler number of compact Kähler manifolds with nonpositive bisectional curvature is proposed, which can be regarded as a complex analogue to the Hopf conjecture.

scholarly journals A Fourth-Order Dispersive Flow into Kähler Manifolds

2015 ◽  
Vol 34 (2) ◽  
pp. 221-249 ◽  
Author(s):  
Hiroyuki Chihara ◽  
Eiji Onodera
Keyword(s):  
Fourth Order ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Dispersive Flow
Sign in / Sign up

Export Citation Format

Share Document