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Izv. RAN. Ser. Mat., 2003, Volume 67, Issue 5, Pages 83–106 (Mi izv452)  

On quasiconformally flat surfaces in Riemannian manifolds

V. M. Miklyukov


Abstract: We establish two properties of $K$-quasiconformally flat hypersurfaces in general Riemannian manifolds. The first is stated in isoperimetric terms and the second in terms of the main frequency of sections of the manifold by geodesic spheres. The two conditions coincide in the two-dimensional case.

DOI: https://doi.org/10.4213/im452

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English version:
Izvestiya: Mathematics, 2003, 67:5, 931–953

Bibliographic databases:

UDC: 517.53/57
MSC: 30C65, 30C70, 35B05
Received: 27.05.2002

Citation: V. M. Miklyukov, “On quasiconformally flat surfaces in Riemannian manifolds”, Izv. RAN. Ser. Mat., 67:5 (2003), 83–106; Izv. Math., 67:5 (2003), 931–953

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  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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