A parabolic flow of balanced metrics
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Lucio Bedulli
und
Luigi Vezzoni
Abstract
We prove a general criterion to establish existence and uniqueness of a short-time solution to an evolution equation involving “closed” sections of a vector bundle, generalizing a method used by Bryant and Xu [8] for studying the Laplacian flow in
Dedicated to the memory of our friend Sergio Console.
Funding statement: This work was supported by the project FIRB “Geometria differenziale e teoria geometrica delle funzioni”, the project PRIN “Varietà reali e complesse: geometria, topologia e analisi armonica” and by G.N.S.A.G.A. of I.N.d.A.M.
Acknowledgements
The authors would like to thank Carlo Mantegazza for useful conversations about parabolic equations on smooth manifolds, and they are very grateful to Enrico Priola for his fundamental help in understanding Hamilton’s paper and to Valentino Tosatti for useful conversations. Moreover, the second author wishes to thank Frederik Witt who, during a useful an important conversation, observed a possible link between the flow considered in the paper and the Calabi flow. Part of the work has been done during a visit of the first author to the University of Turin. The first author is grateful to the University and to the Politecnico of Turin for their hospitality. Finally, we would like to thank an anonymous referee for helping us improve the exposition of the paper.
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© 2017 by De Gruyter
Artikel in diesem Heft
- Frontmatter
- Estimation des dimensions de certaines variétés de Kisin
- A parabolic flow of balanced metrics
- On pliability of del Pezzo fibrations and Cox rings
- The volume of Kähler–Einstein Fano varieties and convex bodies
- The gap phenomenon in parabolic geometries
- Cubic polynomials represented by norm forms
Artikel in diesem Heft
- Frontmatter
- Estimation des dimensions de certaines variétés de Kisin
- A parabolic flow of balanced metrics
- On pliability of del Pezzo fibrations and Cox rings
- The volume of Kähler–Einstein Fano varieties and convex bodies
- The gap phenomenon in parabolic geometries
- Cubic polynomials represented by norm forms
