Overview

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 onthe 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.

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9783662508176

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Reviews

“The area of differential geometry is the main focus of this collection, though it also contains do Carmo’s own commentaries on his life as a scientist as well as assessment of the impact of his research and a complete list of his publications. … His work, as presented in this collection of 32 papers, speaks for itself, as regards both its breadth and its depth, and this volume is an appropriate tribute to him. It is of the highest quality.” (Luiz A. M. Sousa, Jr, Mathematical Reviews, October, 2015) “The volume, with dedication from Professor do Carmo to his students, begins with an overview of do Carmo’s scientific career. … to guide the readers, a complete list of publications until 2010 is included at the end of this volume. This list extends to more than 80 research articles and several books that set milestones in differential geometry. The increase of research on differential geometry in Brazil is thus rigorously documented and the result presented as fundamental reading for this field.” (Corina Mohorianu, Zentralblatt MATH, Vol. 1240, 2012)

The area of differential geometry is the main focus of this collection, though it also contains do Carmo s own commentaries on his life as a scientist as well as assessment of the impact of his research and a complete list of his publications. His work, as presented in this collection of 32 papers, speaks for itself, as regards both its breadth and its depth, and this volume is an appropriate tribute to him. It is of the highest quality. (Luiz A. M. Sousa, Jr, Mathematical Reviews, October, 2015) The volume, with dedication from Professor do Carmo to his students, begins with an overview of do Carmo s scientific career. to guide the readers, a complete list of publications until 2010 is included at the end of this volume. This list extends to more than 80 research articles and several books that set milestones in differential geometry. The increase of research on differential geometry in Brazil is thus rigorously documented and the result presented as fundamental reading for this field. (Corina Mohorianu, Zentralblatt MATH, Vol. 1240, 2012)

Author Information

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 Álvaro 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, thatwas translated into spanish, german and chinese.

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