Book Reviews
Book reviews do not contain an abstract.
You may download the entire review from the links below.
- MathSciNet review: 4076540
- Full text review in PDF
- This review is available free of charge
- Introduction to Global Analysis. Minimal Surfaces in Riemannian Manifolds by John Douglas Moore
- Bull. Amer. Math. Soc. 57 (2020), 353-356
- Additional book information: Graduate Studies in Mathematics, Vol. 187, American Mathematical Society, Providence, RI, 2017, xiv+368 pp., ISBN 978-1-4704-2950-8, $83.00
References
- R. Abraham, Bumpy metrics, Global Analysis (Proc. Sympos. Pure Math., Vols. XIV, XV, XVI, Berkeley, Calif., 1968) Proc. Sympos. Pure Math., XIV-XVI, Amer. Math. Soc., Providence, RI, 1970, pp. 1–3. MR 271994
- Tobias H. Colding and William P. Minicozzi II, Width and finite extinction time of Ricci flow, Geom. Topol. 12 (2008), no. 5, 2537–2586. MR 2460871, DOI 10.2140/gt.2008.12.2537
- Tobias Holck Colding and William P. Minicozzi II, A course in minimal surfaces, Graduate Studies in Mathematics, vol. 121, American Mathematical Society, Providence, RI, 2011. MR 2780140, DOI 10.1090/gsm/121
- H. Blaine Lawson Jr., Lectures on minimal submanifolds. Vol. I, 2nd ed., Mathematics Lecture Series, vol. 9, Publish or Perish, Inc., Wilmington, DE, 1980. MR 576752
- William Meeks III, Leon Simon, and Shing Tung Yau, Embedded minimal surfaces, exotic spheres, and manifolds with positive Ricci curvature, Ann. of Math. (2) 116 (1982), no. 3, 621–659. MR 678484, DOI 10.2307/2007026
- Mario J. Micallef and John Douglas Moore, Minimal two-spheres and the topology of manifolds with positive curvature on totally isotropic two-planes, Ann. of Math. (2) 127 (1988), no. 1, 199–227. MR 924677, DOI 10.2307/1971420
- J. Milnor, Morse theory, Annals of Mathematics Studies, No. 51, Princeton University Press, Princeton, NJ, 1963. Based on lecture notes by M. Spivak and R. Wells. MR 163331
- John Douglas Moore, Bumpy metrics and closed parametrized minimal surfaces in Riemannian manifolds, Trans. Amer. Math. Soc. 358 (2006), no. 12, 5193–5256. MR 2238914, DOI 10.1090/S0002-9947-06-04317-0
- John Douglas Moore, Introduction to global analysis, Graduate Studies in Mathematics, vol. 187, American Mathematical Society, Providence, RI, 2017. Minimal surfaces in Riemannian manifolds. MR 3729450, DOI 10.1090/gsm/187
- Marston Morse, The calculus of variations in the large, American Mathematical Society Colloquium Publications, vol. 18, American Mathematical Society, Providence, RI, 1996. Reprint of the 1932 original. MR 1451874, DOI 10.1090/coll/018
- Robert Osserman, A survey of minimal surfaces, 2nd ed., Dover Publications, Inc., New York, 1986. MR 852409
- Joaquín Pérez, A new golden age of minimal surfaces, Notices Amer. Math. Soc. 64 (2017), no. 4, 347–358. MR 3617312, DOI 10.1090/noti1500
- Jon T. Pitts, Existence and regularity of minimal surfaces on Riemannian manifolds, Mathematical Notes, vol. 27, Princeton University Press, Princeton, NJ; University of Tokyo Press, Tokyo, 1981. MR 626027
- J. Sacks and K. Uhlenbeck, The existence of minimal immersions of $2$-spheres, Ann. of Math. (2) 113 (1981), no. 1, 1–24. MR 604040, DOI 10.2307/1971131
- J. Sacks and K. Uhlenbeck, Minimal immersions of closed Riemann surfaces, Trans. Amer. Math. Soc. 271 (1982), no. 2, 639–652. MR 654854, DOI 10.1090/S0002-9947-1982-0654854-8
- Richard M. Schoen, Analytic aspects of the harmonic map problem, Seminar on nonlinear partial differential equations (Berkeley, Calif., 1983) Math. Sci. Res. Inst. Publ., vol. 2, Springer, New York, 1984, pp. 321–358. MR 765241, DOI 10.1007/978-1-4612-1110-5_{1}7
- R. Schoen and Shing Tung Yau, Existence of incompressible minimal surfaces and the topology of three-dimensional manifolds with nonnegative scalar curvature, Ann. of Math. (2) 110 (1979), no. 1, 127–142. MR 541332, DOI 10.2307/1971247
- S. Smale, An infinite dimensional version of Sard’s theorem, Amer. J. Math. 87 (1965), 861–866. MR 185604, DOI 10.2307/2373250
- 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
- Brian White, The space of minimal submanifolds for varying Riemannian metrics, Indiana Univ. Math. J. 40 (1991), no. 1, 161–200. MR 1101226, DOI 10.1512/iumj.1991.40.40008
Reviewer information
- Reviewer: Tobias Holck Colding
- Affiliation: Mathematics Department, MIT, Cambridge, Massachusetts
- Email: colding@math.mit.edu
Additional Information
- Journal: Bull. Amer. Math. Soc. 57 (2020), 353-356
- DOI: https://doi.org/10.1090/bull/1689
- Published electronically: January 3, 2020
- Review Copyright: © Copyright 2020 American Mathematical Society