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This volume contains the proceedings of the AMS Special Session on Geometry of Submanifolds, in honor or Bang-Yen Chen's 75th birthday, held from October 20-21, 2018, at the University of Michigan, Ann Arbor, Michigan. The development of contemporary geometry of submanifolds benefited greatly from Bang-Yen Chen's contributions, as several interesting questions actively pursued today originate in his work. Chen is known for several fundamental ideas in differential geometry, including Chen inequalities, Chen invariants, Chen's conjectures, Chen surface, Chen-Ricci inequality, Chen submanifolds, Chen equality, submanifolds of finite type, and slant submanifolds. The papers in this volume represent a celebration of the geometry of submanifolds and its connections with other areas of mathematics and cover themes rooted in Chen's work, from investigations on the spectrum of the Laplacian on complete Riemannian manifolds to the geometry of symmetric spaces. These contributions are written with the hope to inform and inspire.
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This volume contains the proceedings of the AMS Special Session on Differential Geometry and Global Analysis, Honoring the Memory of Tadashi Nagano (1930-2017), held January 16, 2020, in Denver, Colorado. Tadashi Nagano was one of the great Japanese differential geometers, whose fundamental and seminal work still attracts much interest today.This volume is inspired by his work and his legacy and, while reminding historical results obtained in the past, presents recent developments in the geometry of symmetric spaces as well as generalizations of symmetric spaces; minimal surfaces and minimal submanifolds; totally geodesic submanifolds and their classification; Riemannian, affine, projective, and conformal connections; the $(M_{+}, M_{-})$ method and its applications; and maximal antipodal subsets. Additionally, the volume features recent achievements related to biharmonic and biconservative hypersurfaces in space forms, the geometry of Laplace operator on Riemannian manifolds, and Chen-Ricci inequalities for Riemannian maps, among other topics that could attract the interest of any scholar working in differential geometry and global analysis on manifolds.
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This volume contains the proceedings of the AMS Special Session on Recent Advanced in Differential Geometry, held virtually on April 1-2, 2023, and the Tenth Congress of Romanian Mathematicians Special Session on Recent Advances in the Geometry of Submanifolds, held on June 30-July 5, 2023, in Pitesti, Romania. In the last two decades, various techniques produced new results in differential geometry and many of them focused on the geometry of submanifolds, where one of the most important questions, the Willmore conjecture, was solved in 2012 by A. Neves and F. Coda Marques. This invites a reflection on the new trends and research directions that contemporary differential geometry might and will take in its natural development. Some of the most important advances have been obtained by using techniques in geometric analysis, while others have been using more classical methods, which are still of interest. Motivated by these new developments, the present volume intends to bring together various viewpoints on the recent study of representing the fundamental idea of space in differential geometry. Of particular interest are the results focused on minimal submanifolds and their generalizations and the related concept of harmonic mappings and their generalizations. In preparing this volume, the editors were particularly interested in the study of curvature functionals in various contexts, from comparison geometry to new curvature invariants, relations between curvature and topology, as well as other related topics.