Pluripotential solutions versus viscosity solutions to complex Monge-Amp{\`e}re flows

TL;DR

This paper demonstrates that different weak solution concepts for degenerate complex Monge-Ampère flows are equivalent and that viscosity solutions match the pluripotential subsolution envelope, unifying key notions in the field.

Contribution

It establishes the equivalence of various weak solution definitions and shows the viscosity solution coincides with the pluripotential subsolution envelope.

Findings

All notions of weak subsolutions coincide.

Viscosity solutions match the envelope of pluripotential subsolutions.

Unification of solution concepts for complex Monge-Ampère flows.

Abstract

We compare various notions of weak subsolutions to degenerate complex Monge-Amp{\`e}re flows, showing that they all coincide. This allows us to show that the viscosity solution coincides with the envelope of pluripotential subsolutions. Dedicated to Duong Hong Phong on the occasion of his 65th birthday.