3 papers
math.AP2026
Regularity of a Geodesic equation in the space of mixed Volume Forms on Hermitian Manifolds
Mathew George
We prove regularity of a fully nonlinear equation that arises from the study of geodesics in the space of mixed volume forms on Hermitian manifolds admitting a balanced metric. Und…
math.AP2024
Fully nonlinear parabolic equations of real forms on Hermitian manifolds
Mathew George, Bo Guan
Over many decades fully nonlinear PDEs, and the complex Monge-Ampère equation in particular played a central role in the study of complex manifolds. Most previous works focused on…
math.DG2024
Volume forms on balanced manifolds and the Calabi-Yau equation
Mathew George
We introduce the space of mixed-volume forms endowed with a metric on a balanced manifold. A geodesic equation can be derived in this space that has an interesting structure…