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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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On the existence and uniqueness of solutions of Möbius equations
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by Xingwang Xu PDF
Trans. Amer. Math. Soc. 337 (1993), 927-945 Request permission

Abstract:

A generalization of the Schwarzian derivative to conformal mappings of Riemannian manifolds has naturally introduced the corresponding overdetermined differential equation which we call the Möbius equation. We are interested in study of the existence and uniqueness of the solution of the Möbius equation. Among other things, we show that, for a compact manifold, if Ricci curvature is nonpositive, for a complete noncompact manifold, if the scalar curvature is a positive constant, then the differential equation has only constant solutions. We also study the nonhomogeneous equation in an $n$-dimensional Euclidean space.
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Additional Information
  • © Copyright 1993 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 337 (1993), 927-945
  • MSC: Primary 58G30; Secondary 53C20, 53C21
  • DOI: https://doi.org/10.1090/S0002-9947-1993-1148047-5
  • MathSciNet review: 1148047