The Yamabe flow on incomplete manifolds

The Yamabe flow on incomplete manifolds J. Evol. Equ. © 2018 Springer International Publishing AG, Journal of Evolution part of Springer Nature Equations https://doi.org/10.1007/s00028-018-0453-3 The Yamabe flow on incomplete manifolds Yuanzhen Shao Abstract. This article is concerned with developing an analytic theory for second-order nonlinear parabolic equations on singular manifolds. Existence and uniqueness of solutions in an L -framework are established by maximal regularity tools. These techniques are applied to the Yamabe flow. It is proven that the Yamabe flow admits a unique local solution within a class of incomplete initial metrics. 1. Introduction Nowadays, there is a rising interest in the study of differential operators on mani- folds with singularities, which is motivated by a variety of applications from applied mathematics, geometry and topology. All the work is more or less related to the semi- nal paper by Kondrat’ev [26]. Among the tremendous amount of the literature on this topic, I would like to mention two lines of research on the study of differential oper- ators of Fuchs type, which have been introduced independently by Melrose [36,37], Nazaikinskii et al. [38], Schulze [45,46] and Schulze and Seiler [47]. One important direction of research on singular analysis is connected with the so-called b-calculus and its http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Evolution Equations Springer Journals

The Yamabe flow on incomplete manifolds

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Publisher
Springer International Publishing
Copyright
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Mathematics; Analysis
ISSN
1424-3199
eISSN
1424-3202
D.O.I.
10.1007/s00028-018-0453-3
Publisher site
See Article on Publisher Site

Abstract

J. Evol. Equ. © 2018 Springer International Publishing AG, Journal of Evolution part of Springer Nature Equations https://doi.org/10.1007/s00028-018-0453-3 The Yamabe flow on incomplete manifolds Yuanzhen Shao Abstract. This article is concerned with developing an analytic theory for second-order nonlinear parabolic equations on singular manifolds. Existence and uniqueness of solutions in an L -framework are established by maximal regularity tools. These techniques are applied to the Yamabe flow. It is proven that the Yamabe flow admits a unique local solution within a class of incomplete initial metrics. 1. Introduction Nowadays, there is a rising interest in the study of differential operators on mani- folds with singularities, which is motivated by a variety of applications from applied mathematics, geometry and topology. All the work is more or less related to the semi- nal paper by Kondrat’ev [26]. Among the tremendous amount of the literature on this topic, I would like to mention two lines of research on the study of differential oper- ators of Fuchs type, which have been introduced independently by Melrose [36,37], Nazaikinskii et al. [38], Schulze [45,46] and Schulze and Seiler [47]. One important direction of research on singular analysis is connected with the so-called b-calculus and its

Journal

Journal of Evolution EquationsSpringer Journals

Published: May 29, 2018

References

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