What type of study is this?

This is a Quantitative Study study.

September 30, 2025Open Access

A new monotone quantity in mean curvature flow implying sharp homotopic criteria

CTChung-Jun TsaiNational Taiwan University MTMao‐Pei TsuiNational Taiwan University MWMu‐Tao WangColumbia University

Puntos clave

The mean curvature flow yields a new monotone quantity under specific conditions, enhancing understanding of manifold behavior.
This quantity proves monotonicity, directing attention towards sharper homotopy criteria for various types of maps.
The study scrutinizes graphical mean curvature flows, particularly in higher codimensions, presenting impactful theoretical advancements.
Implications extend to complex projective spaces, offering insights into the relationships between different manifold mappings.

Resumen

Abstract A new monotone quantity in graphical mean curvature flows of higher codimensions is identified in this work. The submanifold deformed by the mean curvature flow is the graph of a map between Riemannian manifolds, and the quantity is monotone increasing under the area-decreasing condition of the map. The flow provides a natural homotopy of the corresponding map and leads to sharp criteria regarding the homotopic class of maps between complex projective spaces, and maps from spheres to complex projective spaces, among others.

Preguntar a la IA

Me gusta

Guardar

Ver artículo completo