Metric Perspectives of the Ricci Flow Applied to Disjoint Unions

• Autorzy: Sajjad Lakzian , Michael Munn
• Języki publikacji: EN

Abstrakty

EN

In this paper we consider compact, Riemannian manifolds M1, M2 each equipped with a oneparameter family of metrics g1(t), g2(t) satisfying the Ricci flow equation. Adopting the characterization of super-solutions to the Ricci flow developed by McCann-Topping, we define a super Ricci flow for a family of distance metrics defined on the disjoint union M1 ⊔ M2. In particular, we show such a super Ricci flow property holds provided the distance function between points in M1 and M2 is itself a super solution of the heat equation on M1 × M2. We also discuss possible applications and examples.

Słowa kluczowe

EN

super Ricci flow; disjoint union; heat kernel

• Wydawca: De Gruyter Open
• Czasopismo: Analysis and Geometry in Metric Spaces
• Rocznik: 2014
• Tom: 2
• Numer: 1

Daty

otrzymano

2014-03-03

zaakceptowano

2014-10-14

online

2014-11-28

Twórcy

autor

Sajjad Lakzian

• Institutfür Angewandte Mathematik, Universität Bonn, Endenicher Allee 60, 53115 Bonn,Germany

autor

Michael Munn

• University of Missouri, Dept. of Mathematics, Columbia, MO 65201, USA

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Identyfikatory

DOI

10.2478/agms-2014-0011