ﻻ يوجد ملخص باللغة العربية
In recent papers Wu-Yau, Tosatti-Yang and Diverio-Trapani, used some natural differential inequalities for compact Kahler manifolds with quasi negative holomorphic sectional curvature to derive positivity of the canonical bundle. In this note we study the equality case of these inequalities.
We prove two results related to the Schwarz lemma in complex geometry. First, we show that if the inequality in the Schwarz lemmata of Yau, Royden and Tosatti becomes equality at one point, then the equality holds on the whole manifold. In particular
In this note we apply the billiard technique to deduce some results on Viterbos conjectured inequality between volume of a convex body and its symplectic capacity. We show that the product of a permutohedron and a simplex (properly related to each ot
We formulate a Calabi-Yau type conjecture in generalized Kahler geometry, focusing on the case of nondegenerate Poisson structure. After defining natural Hamiltonian deformation spaces for generalized Kahler structures generalizing the notion of Kahl
We propose machine learning inspired methods for computing numerical Calabi-Yau (Ricci flat Kahler) metrics, and implement them using Tensorflow/Keras. We compare them with previous work, and find that they are far more accurate for manifolds with li
We consider the natural generalization of the parabolic Monge-Amp`ere equation to HKT geometry. We prove that in the compact case the equation has always a short-time solution and when the hypercomplex manifold is locally flat and admits a hyperkahle