5 papers
Weak solutions of the generalized Monge-Ampère equation and the supercritical deformed Hermitian-Yang-Mills equation: boundary cases
Rei Murakami
We prove the existence and uniqueness of weak solutions for the generalized Monge-Ampère equation and the supercritical deformed Hermitian-Yang-Mills equation in cohomology classe…
Weak limits of the -flow and the deformed Hermitian-Yang-Mills flow on Kähler surfaces: boundary cases
Rei Murakami
We prove that if a pair of Kähler classes is -nef, the -flow on a compact Kähler surface converges to a weak solution of the Monge-Ampère equation in the sense of currents…
-equations and deformed Hermitian-Yang-Mills equations on holomorphic submersions
Rei Murakami
In this paper, we prove that there exists a solution of the -equation on the total space of a holomorphic submersion if there exist solutions of the -equation on the fibers a…
Numerical criteria on the complex Hessian quotient equations with the Calabi symmetry
Rei Murakami
Assuming Calabi symmetry, we prove that a numerical condition ensures the solvability of the complex Hessian quotient equation, as conjectured by Székelyhidi. We also propose a co…
An analytic proof of Griffiths' conjecture on compact Riemann surfaces
Rei Murakami
Griffiths' conjecture asserts that a holomorphic vector bundle is ample if and only if it admits a Hermitian metric with positive curvature. In this paper, we present a new proof o…