Geometry at Infinity
Description
This volume contains a collection of survey and research papers written by experts in differential geometry, geometric topology, and global analysis. It provides an overview of recent developments related to the theme Geometry at Infinity. Special emphasis is placed on the interconnections between these different fields. The papers are written for graduate students and researchers with a general interest in geometry who wish to keep abreast of current trends in these central areas of modern mathematics.
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Persons
Christian Bär held professorships in Freiburg and Hamburg and is now a professor of geometry at the University of Potsdam. He works in differential geometry and applications to mathematical physics. He was the president of the German Mathematical Society and, in addition to his work in research and teaching, is the editor-in-chief of zbMATH Open.
Bernhard Hanke has held the Chair of Differential Geometry at the University of Augsburg since 2010. Prior to this, he was a professor at the Technical University of Munich (TUM). His research interests include differential geometry and topology, with a particular focus on scalar curvature geometry. From 2016 to 2026, he served as the coordinator of the DFG-funded Priority Programme Geometry at Infinity .
Anna Wienhard is a director at the Max Planck Institute for Mathematics in the Sciences in Leipzig. Her research explores geometric structures, Lie groups and their discrete subgroups, and higher Teichmüller spaces. She has been awarded a Sloan fellowship, the Hector Science Award and several ERC grants. She is a Fellow of the American Mathematical Society, a member of the German National Academy of Sciences Leopoldina and several other academies.
Burkhard Wilking was a professor at the University of Pennsylvania before moving to his current position in Münster in 2002. He works in differential geometry, in particular, on lower curvature bounds and Ricci flow. He has been awarded a Sloan fellowship, the Leibniz prize and the Staudt prize.
Content
Part I. Large-scale geometry and asymptotic invariants.- Chapter 1. Large-scale geometry and asymptotic invariants.- Chapter 2. On the asymptotic equidistribution of word values in symmetric groups.- Chapter 3. Geometric invariants of local and arithmetic solvable groups.- Chapter 4. Infinite groups from the profinite point of view.- Chapter 5. Graphs at infinity: Liouville theorems, recurrence and characterization of Dirichlet Forms.- Chapter 6. Transgressing the algebraic coarse character map.- Chapter 7. Duality pairings with the analytic structure group.- Chapter 8. L2-invariants and Thurston's vision.- Chapter 9. An invitation to fine curve graphs.- Chapter 10. Similarities between Euclidean Buildings and Riemannian Symmetric Spaces of Non-Compact Type.- Chapter 11. The geometry of branched covers of hyperbolic manifolds.- Part II. Moduli spaces and geometric structures.- Chapter 12. Axiom A flows and dynamical resonances for Anosov representations.- Chapter 13. Rigidity, deformations and limits of maximal representations.- Chapter 14. Asymptotic geometry of the Higgs bundle moduli space.- Chapter 15. Variations of stability and hyper-Kähler structures on moduli of parabolic Higgs Bundles.- Chapter 16. Self-duality solutions near infinity.- Chapter 17. Hypercomplex analytic spaces and schemes.- Chapter 18. Twistor geometric aspects of projective surfaces.- Part III. Curvature and topology.- Chapter 19. Spaces and Moduli Spaces of Metrics with Lower Curvature Bounds.- Chapter 20. The space of psc-concordances.- Chapter 21. Callias operators and quantitative metric inequalities with scalar curvature.- Chapter 22. Highly connected 7-manifolds, the linking form and non-negative curvature.- Chapter 23. Topology of Alexandrov Spaces with Cohomogeneity One Actions.- Chapter 24. Singular Riemannian foliations and collapse.- Chapter 25. Ricci flow and the scalar curvature rigidity of Einstein manifolds.- Chapter 26. Einstein metrics, their moduli spaces and stability.- Part IV. Geometric analysis and relativity.- Chapter 27. Synthetic notions of Ricci flow for metric measure spaces.- Chapter 28. Minimal surfaces in metric spaces.- Chapter 29. Nonunique tangent maps at isolated singularities of minimizing p-harmonic maps.- Chapter 30. Flowing Shapes: Theory and some Trends in the volume preserving Mean Curvature Flow and the Willmore Functional.- Chapter 31. Noncompact mean curvature flows.- Chapter 32. Evolution Equations on Manifolds with Conical Singularities.- Chapter 33. Solutions to Ricci flow whose scalar curvature is in Lp.- Chapter 34. Capillary hypersurfaces: Minkowski formulas, geometric inequalities and capillary Gauss curvature flow.- Chapter 35. A hitchhiker's guide to first-order elliptic boundary value problems.- Chapter 36. Analysis on fibred cusp spaces.- Chapter 37. Some aspects of the spectral theory with twisting representations.- Chapter 38. Heat kernel asymptotics for quaternionic contact manifolds.- Chapter 39. On the construction of non time-symmetric initial data sets.- Chapter 40. Geometrically defined asymptotic coordinates in General Relativity.- Chapter 41. Homogeneous spacetimes inspired from Margulis spacetimes.