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Geometriae Dedicata

, Volume 191, Issue 1, pp 137–151 | Cite as

A flow approach to the fractional Minkowski problem

  • Alina Stancu
  • Shardul Vikram
Original Paper

Abstract

We study the asymptotic behaviour of a planar, anisotropic curvature flow and use it to provide a new proof for the existence of solutions to the smooth, planar \(L_p\)-Minkowski problem with \(0< p <1\).

Keywords

Asymptotic behaviour Convex bodies Curvature flows Planar Minkowski problem 

Mathematics Subject Classification (2010)

Primary 53C44 52A05 Secondary 35K55 

Notes

Acknowledgements

The authors are thankful to the reviewers for their comments on the paper which improved the original manuscript.

Funding The first author’s research was supported by a Natural Sciences and Engineering Research Council of Canada award (Grant No. 327635-2012).

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Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsConcordia UniversityMontrealCanada

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