Advances in Submanifold Theory and Related Topics

This contributed volume collects articles by specialists in submanifold theory, geometric analysis, and Riemannian geometry, with contributors from four continents. It is dedicated to Professor Marcos Dajczer, whose research and teaching activities have influenced new generations of geometers. Some of the works contained in this volume are written by his mathematical descendants and reflect the state of the art and current discussion in the field.

Now retired from the Institute of Pure and Applied Mathematics (IMPA), Brazil, but still active, Professor Dajczer has conducted research in these and other fields, contributing to the development of submanifold theory in Brazil. He completed his undergraduate studies at the University of Buenos Aires, Argentina, in 1975, and received his PhD in Mathematics from IMPA in 1980. A postdoctoral period at the State University of New York in Stony Brook marked the beginning of a fruitful collaboration with Prof. D. Gromoll that lasted several years.

Prof. Dajczer and Dr. Ruy Tojeiro are co-authors of the textbook Submanifold Theory: Beyond an Introduction, which is available in Springer's Universitext series.

Celebrates Prof. Dajczer's contributions and influence in the development of research on this topic Gathers selected contributions from his mathematical descendants across four continents Features in-depth discussions on relevant topics in the field

Autorentext

Ruy Tojeiro is a Full Professor at the Institute of Mathematics and Computer Science (ICMC) at the University of São Paulo in São Carlos, Brazil. He holds a PhD in Mathematics from the Institute of Pure and Applied Mathematics (IMPA), Brazil. His research focuses on differential geometry, particularly on submanifolds.

Inhalt

Preface.- The Dirichlet problem for the minimal surface equation on unbounded helicoidal domains of R^m.- Maximum principles for weakly 1-coercive operators with applications to capillary and prescribed mean curvature graphs.- The intrinsic metric of constant mean curvature surfaces and minimal hypersurfaces with free boundary.- Conformally Einstein left-invariant metrics on four-dimensional Lie groups.- On the propagation of singularities of constant curvature, convex hypersurfaces.- Ribaucour partial tubes and hypersurfaces of Enneper type.- Conformal immersions of product manifolds endowed with polar metrics.- Compact flat manifolds and reducibility.- Elementary proof of a Lemma for parallel mean curvature surfaces in complex space forms.