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Izv. Akad. Nauk SSSR Ser. Mat., 1972, Volume 36, Issue 5, Pages 1049–1079 (Mi izv2345)  

This article is cited in 10 scientific papers (total in 10 papers)

Minimal compacta in riemannian manifolds and Reifenberg's conjecture

A. T. Fomenko


Abstract: In this paper one obtains a geometrical lower bound on the measure of an arbitrary minimal compactum which realizes an arbitrary nontrivial cocycle in a compact riemannian manifold. In particular, one gets an answer to Reifenberg's question about the number of “leaves” at singular points of special types, and concrete examples are also given of global minimal compacta in symmetric spaces.

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English version:
Mathematics of the USSR-Izvestiya, 1972, 6:5, 1037–1066

Bibliographic databases:

UDC: 513.83
MSC: Primary 49F10; Secondary 53C35
Received: 29.10.1971

Citation: A. T. Fomenko, “Minimal compacta in riemannian manifolds and Reifenberg's conjecture”, Izv. Akad. Nauk SSSR Ser. Mat., 36:5 (1972), 1049–1079; Math. USSR-Izv., 6:5 (1972), 1037–1066

Citation in format AMSBIB
\Bibitem{Fom72}
\by A.~T.~Fomenko
\paper Minimal compacta in riemannian manifolds and Reifenberg's conjecture
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1972
\vol 36
\issue 5
\pages 1049--1079
\mathnet{http://mi.mathnet.ru/izv2345}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=333901}
\zmath{https://zbmath.org/?q=an:0282.49040}
\transl
\jour Math. USSR-Izv.
\yr 1972
\vol 6
\issue 5
\pages 1037--1066
\crossref{https://doi.org/10.1070/IM1972v006n05ABEH001911}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Yu. A. Aminov, “On the instability of a minimal surface in an $n$-dimensional Riemannian space of positive curvature”, Math. USSR-Sb., 29:3 (1976), 359–375  mathnet  crossref  mathscinet  zmath  isi
    2. Dào Trong Thi, “Minimal real currents on compact Riemannian manifolds”, Math. USSR-Izv., 11:4 (1977), 807–820  mathnet  crossref  mathscinet  zmath
    3. A. T. Fomenko, “On minimal volumes of topological globally minimal surfaces in cobordisms”, Math. USSR-Izv., 18:1 (1982), 163–183  mathnet  crossref  mathscinet  zmath
    4. A. T. Fomenko, “Multi-dimensional variational methods in the topology of extremals”, Russian Math. Surveys, 36:6 (1981), 127–165  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. Lê Hông Vân, “Minimal surfaces in homogeneous spaces”, Math. USSR-Izv., 32:2 (1989), 413–427  mathnet  crossref  mathscinet  zmath
    6. Herman Gluck, Frank Morgan, Wolfgang Ziller, “Calibrated geometries in Grassmann manifolds”, Comment Math Helv, 64:1 (1989), 256  crossref  mathscinet  zmath  isi
    7. A. O. Ivanov, “Calibration forms and new examples of stable and globally minimal surfaces”, Math. USSR-Sb., 71:2 (1992), 289–308  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    8. Vincent Borrelli, Olga Gil-Medrano, “Area-minimizing vector fields on round 2-spheres”, Journal für die reine und angewandte Mathematik (Crelles Journal), 2010:640 (2010), 85  crossref
    9. A. O. Ivanov, A. A. Tuzhilin, “One-dimensional Gromov minimal filling problem”, Sb. Math., 203:5 (2012), 677–726  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    10. A. Yu. Eremin, “A formula for the weight of a minimal filling of a finite metric space”, Sb. Math., 204:9 (2013), 1285–1306  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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