Abstract
We investigate the properties of the modulus of a foliation on a Riemannian manifold. We give necessary and sufficient conditions for the existence of the extremal function and state some of its properties. We obtain an integral formula which, in a sense, combines the integral over the manifold with the integral over the leaves. We state a relation between the extremal function and the geometry of the distribution orthogonal to a foliation.
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This article is based on a part of author’s PhD Thesis [11]. The author wishes to thank her advisor Professor Antoni Pierzchalski who suggested the problem under consideration in this paper and for helpful discussions. The author wishes to thank Kamil Niedziałomski for helpful discussions that led to improvements of some of the theorems. In addition, the author wishes to thank anonymous referee for many useful comments, especially the ones included in Remark 3.
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Ciska-Niedziałomska, M. On the extremal function of the modulus of a foliation. Arch. Math. 107, 89–100 (2016). https://doi.org/10.1007/s00013-016-0913-3
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DOI: https://doi.org/10.1007/s00013-016-0913-3