Rationally connected manifolds and semipositivity of the Ricci curvature

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Compact K¨ ahler manifolds with semipositive anticanonical bundles have been studied in depth in [CDP12], where a rather general structure theorem for this type of manifolds has

Under volume growth, diameter or density of rays conditions, some results were obtained on the geometry and topology of open manifolds with nonnegative Ricci curvature... Abresch

In fact, using a very recent result of Paul [26] and the same arguments as those in the proof of Theorem 6.1, we can prove directly that the K-energy is proper along the K¨

In this section, we prove an important estimate between the local upper bound near a fiber X y of the Riemann curvature of a particular K¨ahler-Ricci flow solution and the local

Let us now describe our results in more precise PDE terms. Theorem 3.3 en- ables us to obtain global bounds for gradients when the growth for the minimal graphic functions is

By refining the Bochner formulas for any Hermitian complex vector bundle (and Riemannian real vector bundle) with an arbitrary metric connection over a compact Hermitian manifold,

In this paper, we give sufficient and necessary conditions for the existence of a K¨ ahler–Einstein metric on a quasi-projective man- ifold of finite volume, bounded Riemannian