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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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


On the singular structure of three-dimensional, area-minimizing surfaces
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by Frank Morgan PDF
Trans. Amer. Math. Soc. 276 (1983), 137-143 Request permission


A sufficient condition is given for the union of two three-dimensional planes through the origin in ${{\mathbf {R}}^n}$ to be area-minimizing. The condition is in terms of the three angles $0 \leqslant {\gamma _1} \leqslant {\gamma _2} \leqslant {\gamma _3}$ which characterize the geometric relationship between the planes. If ${\gamma _3} \leqslant {\gamma _1} + {\gamma _2}$, the union of the planes is area-minimizing.
    F. J. Almgren, Jr., Multiple valued functions minimizing Dirichlet’s integral and the regularity of mass minimizing integral currents (in preparation).
  • Robert L. Bryant, Submanifolds and special structures on the octonians, J. Differential Geometry 17 (1982), no. 2, 185–232. MR 664494
  • Herbert Federer, Geometric measure theory, Die Grundlehren der mathematischen Wissenschaften, Band 153, Springer-Verlag New York, Inc., New York, 1969. MR 0257325
  • Reese Harvey and Blaine Lawson, Student reminiscences of Kodaira at Stanford, Asian J. Math. 4 (2000), no. 1, iv. Kodaira’s issue. MR 1803726
  • Frank Morgan, On the singular structure of two-dimensional area minimizing surfaces in $\textbf {R}^{n}$, Math. Ann. 261 (1982), no. 1, 101–110. MR 675210, DOI 10.1007/BF01456413
  • Jean E. Taylor, The structure of singularities in soap-bubble-like and soap-film-like minimal surfaces, Ann. of Math. (2) 103 (1976), no. 3, 489–539. MR 428181, DOI 10.2307/1970949
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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 276 (1983), 137-143
  • MSC: Primary 49F20; Secondary 53A10
  • DOI:
  • MathSciNet review: 684498