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.DG2025
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…
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…