This volume of selected academic papers demonstrates the significance of the contribution to mathematics made by Manfredo P. do Carmo. Twice a Guggenheim Fellow and the winner of many prestigious national and international awards, the professor at the institute of Pure and Applied Mathematics in Rio de Janeiro is well known as the author of influential textbooks such as Differential Geometry of Curves and Surfaces. The area of differential geometry is the main focus of this selection, though it also contains do Carmo's own commentaries on his life as a scientist as well as assessment of the impact of his researches and a complete list of his publications. Aspects covered in the featured papers include relations between curvature and topology, convexity and rigidity, minimal surfaces, and conformal immersions, among others. Offering more than just a retrospective focus, the volume deals with subjects of current interest to researchers, including a paper co-authored with Frank Warner on the convexity of hypersurfaces in space forms. It also presents the basic stability results for minimal surfaces in the Euclidean space obtained by the author and his collaborators. Edited by do Carmo's first student, now a celebrated academic in her own right, this collection pays tribute to one of the most distinguished mathematicians.
Manfredo P. do Carmo is Professor Emeritus at IMPA, Rio de Janeiro. He graduated as a Civil Engineer in Recife, Brazil and he completed his PhD, in 1963, under the supervision of S.S. Chern, at the University of California, Berkeley. He has held visiting positions in several universities in Brazil and abroad. He is a member of the Brazilian Academy of Sciences and of TWAS and he received several prizes. Amog them the Almirante Alvaro Alberto prize from the Brazilian Research Council (CNPq), the mathematics Prize of TWAS and the Brazilian National Order of Scientific Merit. He has served as President of the Brazilian Mathematical Society, as a member of the Selecting Committee of the Brazilian Academy of Sciences, and as Chairman of the Mathematics Committee of CAPES, at the Ministry of Education . He has published several research articles and books on Differential Geometry. One of his books is the well known textbook on Differential Geometry of Curves and Sufaces, that was translated into spanish, german and chinese.
Preface.- A Summary of the Scientific Activities of Manfredo P. do Carmo.- Summary of thePapers in this Volume by Manfredo P. do Carmo.- Contributions.- Complete List of Publications of Manfredo P. do Carmo.- List of D.Sc. Students of Manfredo P. do Carmo.