Results 1  10
of
30
A BrunnMinkowski type inequality for Fano manifolds and the BandoMabuchi uniqueness theorem
"... ar ..."
Viscosity solutions to degenerate complex MongeAmpère equations
, 2010
"... Degenerate complex MongeAmpère equations on compact Kähler manifolds have been recently intensively studied using tools from pluripotential theory. We develop an alternative approach based on the concept of viscosity solutions and compare systematically viscosity concepts with pluripotential theor ..."
Abstract

Cited by 19 (7 self)
 Add to MetaCart
Degenerate complex MongeAmpère equations on compact Kähler manifolds have been recently intensively studied using tools from pluripotential theory. We develop an alternative approach based on the concept of viscosity solutions and compare systematically viscosity concepts with pluripotential theoretic ones. This approach works only for a rather restricted type of degenerate complex MongeAmpère equations. Nevertheless, we prove that the local potentials of the singular KählerEinstein metrics constructed previously by the authors are continuous plurisubharmonic functions. They were previously known to be locally bounded. Another application is a lower order construction with a C 0estimate of the solution to the Calabi conjecture which does not use Yau’s celebrated theorem.
MoserTrudinger type inequalities for complex MongeAmpère operators and Aubins hypothèse fondamentale
"... ar ..."
(Show Context)
Holomorphic Morse inequalities and asymptotic cohomology groups: a tribute to Bernhard Riemann
 IN THE PROCEEDINGS OF THE RIEMANN INTERNATIONAL SCHOOL OF MATHEMATICS, ADVANCES IN NUMBER THEORY AND GEOMETRY, HELD AT VERBANIA
, 2009
"... The goal of this note is to present the potential relationships between certain MongeAmpère integrals appearing in holomorphic Morse inequalities, and asymptotic cohomology estimates for tensor powers of line bundles, as recently introduced by algebraic geometers. The expected most general statemen ..."
Abstract

Cited by 7 (4 self)
 Add to MetaCart
The goal of this note is to present the potential relationships between certain MongeAmpère integrals appearing in holomorphic Morse inequalities, and asymptotic cohomology estimates for tensor powers of line bundles, as recently introduced by algebraic geometers. The expected most general statements are still conjectural and oweadebt to Riemann’s pioneering work, which ledto the concept of Hilbert polynomials and to the HirzebruchRiemannRoch formula during the XXth century.
On Pointwise Gradient estimates for the complex MongeAmpère equation
 in Advances in Geometric Analysis, 87–96, Adv. Lect. Math. (ALM) 21, International
, 2012
"... ar ..."