Opening note: An homage to Manfredo P. do Carmo
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ening note: An homage to Manfredo P. do Carmo Claudio Gorodski1 · Paolo Piccione1 Accepted: 6 October 2020 © Instituto de Matemática e Estatística da Universidade de São Paulo 2020
Over 100 mathematicians from Brazil and abroad took part in the ICM2018 Satellite Conference Modern Trends in Differential Geometry (MTDG) held at the University of São Paulo on 23–27 July 2018.1 As an homage of São Paulo to the doyen of Differential Geometry in Brazil, we at the São Paulo Journal of Mathematical Sciences have decided to dedicate a special section in this issue, containing selected contributions from participants in the conference, to the memory of Manfredo Perdigão do Carmo (1928–2018).
Do Carmo in Berkeley in 19792 1 We acknowledge generous financial support from Fapesp (Grant No. 2017/18467-3) and CAPES (AUXPE No. 0439/2018, Grant No. 88881.154934/2017-01). 2 Attribution: George Bergmann, https://commons.wikimedia.org/wiki/File:Manfredo_do_Carmo _1979_(headshot,_enlarged).jpg, Creative Commons Attribution-Share Alike 4.0 International
* Claudio Gorodski [email protected] 1
Universidade de São Paulo, São Paulo, Brazil
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Student of S.-S. Chern in Berkeley (1963) and speaker of the ICM1978 in Helsinki, the name of do Carmo is known for his many contributions to Riemannian manifolds, topology of manifolds, rigidity and convexity of isometric immersions, minimal surfaces, stability of hypersurfaces, isoperimetric problems, minimal submanifolds of spheres, and manifolds of constant mean curvature and vanishing scalar curvature. His legacy is also witnessed by his textbooks translated into many languages and used in courses from universities such as Harvard and Columbia, and his students that include Celso Costa, Marcos Dajczer and Keti Tenenblat. Eighteen invited speakers presented one-hour talks in MTDG, with subjects in different flavors of geometry, interacting with algebra, topology and analysis, so much characteristic for the mathematical thinking of do Carmo. Further, the program included a large poster session as well as a one hour and a half long problem session, moderated by Frank Morgan and Pierre Pansu, who also coauthor a valuable article in this special section containing a transcription of the proposed problems. We heartly thank all the people that submitted contributions to this homage and we hope that readers will enjoy the variety of points of view and insights.
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