Existence of Ricci Flows of Incomplete Surfaces

By Gregor Giesen, P. Topping. 2010

106 citations recorded by the source corpus.

We prove a general existence result for instantaneously complete Ricci flows starting at an arbitrary Riemannian surface which may be incomplete and may have unbounded curvature. We give an explicit formula for the maximal existence time, and describe the asymptotic behaviour in most cases.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/ee379810aaba7e7c21e286a4ae41e466b47fbc51

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Esther Cabezas-Rivas
2. Burkhard Wilking
3. P. Topping
4. Miaomiao Zhu
5. W. Ziller
6. W. Wylie
7. Peter Petersen
8. Valentino Tosatti

In Astronomy and Astrophysics

1. Esther Cabezas-Rivas
2. Burkhard Wilking
3. P. Topping
4. Valentino Tosatti
5. Peter Petersen
6. Frederick Wilhelm

In Geometry and Topology

1. Esther Cabezas-Rivas
2. Burkhard Wilking
3. P. Topping
4. Miaomiao Zhu
5. W. Ziller
6. W. Wylie
7. Peter Petersen
8. Marco Radeschi

Citations in the corpus

• How to produce a Ricci Flow via Cheeger-Gromoll exhaustion (2011, methodology): “Giesen and Topping [21] gave immortal 2-dimensional Ricci flows with unbounded curvature for all time.”
• Ricci flow compactness via pseudolocality, and flows with incomplete initial metrics (2010, background): “In particular, a uniqueness result was proved in [9] and a more refined existence result can be found in [10].”