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Geometric Probability on the Sphere

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Abstract

This is an exposition of results and methods from geometric probability on the surface of a ball (i.e., on a sphere) in three-dimensional space. We tried to make our arguments simple and intuitive. We present many concrete results together with their (mainly) elementary proofs, and also several new results are derived. In addition, the reader will also find various interesting unsolved problems.

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Acknowledgements

The authors wish to thank the referee for his careful reading of the manuscript and for his useful comments.

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Authors and Affiliations

  1. Ryukyu University, Nishihara, Okinawa, 903-0213, Japan

    Hiroshi Maehara

  2. Faculty of Mathematics, Chemnitz University of Technology, 09107, Chemnitz, Germany

    Horst Martini

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  1. Hiroshi Maehara
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  2. Horst Martini
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Correspondence to Horst Martini.

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Maehara, H., Martini, H. Geometric Probability on the Sphere. Jahresber. Dtsch. Math. Ver. 119, 93–132 (2017). https://doi.org/10.1365/s13291-017-0158-5

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