Ricci flows with unbounded curvature

TL;DR

This paper demonstrates that every noncompact Riemann surface can support a complete Ricci flow with unbounded curvature at all times, expanding understanding of Ricci flow behavior on noncompact surfaces.

Contribution

It constructs explicit Ricci flows on noncompact Riemann surfaces that maintain unbounded curvature throughout their evolution, a novel existence result.

Findings

Existence of complete Ricci flows with unbounded curvature on all noncompact Riemann surfaces.

Unbounded curvature persists for all times in the constructed flows.

Provides new examples of Ricci flows with unbounded curvature in noncompact settings.

Abstract

We show that any noncompact Riemann surface admits a complete Ricci flow g(t), t\in[0,\infty), which has unbounded curvature for all t\in[0,\infty).