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Curvature Measures, Isoperimetric Type Inequalities and Fully Nonlinear PDEs

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Fully Nonlinear PDEs in Real and Complex Geometry and Optics

Part of the book series: Lecture Notes in Mathematics ((LNMCIME,volume 2087))

Abstract

The notes consider two special fully nonlinear partial differential equations arising from geometric problems, one is of elliptic type and another is of parabolic type. The elliptic equation is associated to the problem of prescribing curvature measures, while an inverse mean curvature type of parabolic equation is introduced to prove the isoperimetric type inequalities for quermassintegrals of k-convex starshaped domains.

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Acknowledgements

Large part of the material in this lecture notes are based on joint works with Junfang Li [17, 27]. I would like to thank him for many helpful discussions and valuable comments regarding the exposition of the notes. Research of the first author was supported in part by an NSERC Discovery Grant.

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  1. Department of Mathematics, McGill University, Montreal, QC, H3A 2K6, Canada

    Pengfei Guan

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Guan, P. (2014). Curvature Measures, Isoperimetric Type Inequalities and Fully Nonlinear PDEs. In: Fully Nonlinear PDEs in Real and Complex Geometry and Optics. Lecture Notes in Mathematics(), vol 2087. Springer, Cham. https://doi.org/10.1007/978-3-319-00942-1_2

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