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- Extrinsic geometric flows by Ben Andrews, Bennett Chow, Christine Guenther and Mat Langford
- Bull. Amer. Math. Soc. 59 (2022), 145-154
- Additional book information: Graduate Studies in Mathematics, Vol. 206, American Mathematical Society, Providence, RI, 2020, xxv+759 pp., ISBN 978-1-4704-5596-5
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- Ben Andrews and Paul Bryan, Curvature bounds by isoperimetric comparison for normalized Ricci flow on the two-sphere, Calc. Var. Partial Differential Equations 39 (2010), no. 3-4, 419–428. MR 2729306, DOI 10.1007/s00526-010-0315-5
- Ben Andrews, Pengfei Guan, and Lei Ni, Flow by powers of the Gauss curvature, Adv. Math. 299 (2016), 174–201. MR 3519467, DOI 10.1016/j.aim.2016.05.008
- Edwin F. Beckenbach and Richard Bellman, Inequalities, Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Band 30, Springer-Verlag, Inc., New York, 1965. Second revised printing. MR 0192009
- Wilhelm Blaschke, Kreis und Kugel, Walter de Gruyter & Co., Berlin, 1956 (German). 2te Aufl. MR 0077958
- Károly J. Böröczky, Erwin Lutwak, Deane Yang, and Gaoyong Zhang, The logarithmic Minkowski problem, J. Amer. Math. Soc. 26 (2013), no. 3, 831–852. MR 3037788, DOI 10.1090/S0894-0347-2012-00741-3
- Simon Brendle, Kyeongsu Choi, and Panagiota Daskalopoulos, Asymptotic behavior of flows by powers of the Gaussian curvature, Acta Math. 219 (2017), no. 1, 1–16. MR 3765656, DOI 10.4310/ACTA.2017.v219.n1.a1
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- Eugenio Calabi, Improper affine hyperspheres of convex type and a generalization of a theorem by K. Jörgens, Michigan Math. J. 5 (1958), 105–126. MR 106487
- Shiing-shen Chern, A simple intrinsic proof of the Gauss-Bonnet formula for closed Riemannian manifolds, Ann. of Math. (2) 45 (1944), 747–752. MR 11027, DOI 10.2307/1969302
- Kai-Seng Chou and Xu-Jia Wang, A logarithmic Gauss curvature flow and the Minkowski problem, Ann. Inst. H. Poincaré C Anal. Non Linéaire 17 (2000), no. 6, 733–751. MR 1804653, DOI 10.1016/S0294-1449(00)00053-6
- Kai-Seng Chou and Xi-Ping Zhu, The curve shortening problem, Chapman & Hall/CRC, Boca Raton, FL, 2001. MR 1888641, DOI 10.1201/9781420035704
- Tobias Holck Colding, William P. Minicozzi II, and Erik Kjær Pedersen, Mean curvature flow, Bull. Amer. Math. Soc. (N.S.) 52 (2015), no. 2, 297–333. MR 3312634, DOI 10.1090/S0273-0979-2015-01468-0
- Klaus Ecker, Regularity theory for mean curvature flow, Progress in Nonlinear Differential Equations and their Applications, vol. 57, Birkhäuser Boston, Inc., Boston, MA, 2004. MR 2024995, DOI 10.1007/978-0-8176-8210-1
- William J. Firey, Shapes of worn stones, Mathematika 21 (1974), 1–11. MR 362045, DOI 10.1112/S0025579300005714
- Dmitry Fuchs and Serge Tabachnikov, Mathematical omnibus, American Mathematical Society, Providence, RI, 2007. Thirty lectures on classic mathematics. MR 2350979, DOI 10.1090/mbk/046
- Yoshikazu Giga, Surface evolution equations, Monographs in Mathematics, vol. 99, Birkhäuser Verlag, Basel, 2006. A level set approach. MR 2238463
- Pengfei Guan and Junfang Li, The quermassintegral inequalities for $k$-convex starshaped domains, Adv. Math. 221 (2009), no. 5, 1725–1732. MR 2522433, DOI 10.1016/j.aim.2009.03.005
- Pengfei Guan and Lei Ni, Entropy and a convergence theorem for Gauss curvature flow in high dimension, J. Eur. Math. Soc. (JEMS) 19 (2017), no. 12, 3735–3761. MR 3730513, DOI 10.4171/JEMS/752
- G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1988. Reprint of the 1952 edition. MR 944909
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- Hans Lewy, On differential geometry in the large. I. Minkowski’s problem, Trans. Amer. Math. Soc. 43 (1938), no. 2, 258–270. MR 1501942, DOI 10.1090/S0002-9947-1938-1501942-3
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- John W. Milnor, Topology from the differentiable viewpoint, Princeton Landmarks in Mathematics, Princeton University Press, Princeton, NJ, 1997. Based on notes by David W. Weaver; Revised reprint of the 1965 original. MR 1487640
- Lei Ni, Monotonicity and Li-Yau-Hamilton inequalities, Surveys in differential geometry. Vol. XII. Geometric flows, Surv. Differ. Geom., vol. 12, Int. Press, Somerville, MA, 2008, pp. 251–301. MR 2488944, DOI 10.4310/SDG.2007.v12.n1.a7
- Louis Nirenberg, The Weyl and Minkowski problems in differential geometry in the large, Comm. Pure Appl. Math. 6 (1953), 337–394. MR 58265, DOI 10.1002/cpa.3160060303
- V. V. Nikulin and I. R. Shafarevich, Geometries and groups, Universitext, Springer-Verlag, Berlin, 1987. Translated from the Russian by M. Reid; Springer Series in Soviet Mathematics. MR 917939, DOI 10.1007/978-3-642-61570-2
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- Reviewer: Lei Ni
- Affiliation: Department of Mathematics, University of California, San Diego,La Jolla, California 92093
- Email: leni@ucsd.edu
- Journal: Bull. Amer. Math. Soc. 59 (2022), 145-154
- DOI: https://doi.org/10.1090/bull/1740
- Published electronically: June 17, 2021
- Review Copyright: © Copyright 2021 American Mathematical Society