Browsing by Author "Hanke, Bernhard"

Now showing 1 - 5 of 5
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    Analysis, Geometry and Topology of Positive Scalar Curvature Metrics
    (Zürich : EMS Publ. House, 2014) Hanke, Bernhard; Neves, Andre
    One of the fundamental problems in Riemannian geometry is to understand the relation of locally defined curvature invariants and global properties of smooth manifolds. This workshop was centered around the investigation of scalar curvature, addressing questions in global analysis, geometric topology, relativity and minimal surface theory.
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    Analysis, Geometry and Topology of Positive Scalar Curvature Metrics
    (Zürich : EMS Publ. House, 2017) Hanke, Bernhard; Neves, André
    Riemannian manifolds with positive scalar curvature play an important role in mathematics and general relativity. Obstruction and existence results are connected to index theory, bordism theory and homotopy theory, using methods from partial differential equations and functional analysis. The workshop led to a lively interaction between mathematicians working in these areas.
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    Analysis, Geometry and Topology of Positive Scalar Curvature Metrics
    (Zürich : EMS Publ. House, 2024) Ammann, Bernd; Hanke, Bernhard; Sakovich, Anna
    Riemannian metrics with positive scalar curvature play an important role in differential geometry and general relativity. To investigate these metrics, it is necessary to employ concepts and techniques from global analysis, geometric topology, metric geometry, index theory, and general relativity. This workshop brought together researchers from a variety of backgrounds to combine their expertise and promote cross-disciplinary exchange.
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    Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (hybrid meeting)
    (Zürich : EMS Publ. House, 2021) Hanke, Bernhard; Sakovich, Anna
    The investigation of Riemannian metrics with lower scalar curvature bounds has been a central topic in differential geometry for decades. It addresses foundational problems, combining ideas and methods from global analysis, geometric topology, metric geometry and general relativity. Seminal contributions by Gromov during the last years have led to a significant increase of activities in the area which have produced a number of impressive results. Our workshop reflected the state of the art of this thriving field of research.
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    Boundary Conditions for Scalar Curvature
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2021) Bär, Christian; Hanke, Bernhard
    Based on the Atiyah-Patodi-Singer index formula, we construct an obstruction to positive scalar curvature metrics with mean convex boundaries on spin manifolds of infinite K-area. We also characterize the extremal case. Next we show a general deformation principle for boundary conditions of metrics with lower scalar curvature bounds. This implies that the relaxation of boundary conditions often induces weak homotopy equivalences of spaces of such metrics. This can be used to refine the smoothing of codimension-one singularites à la Miao and the deformation of boundary conditions à la Brendle-Marques-Neves, among others. Finally, we construct compact manifolds for which the spaces of positive scalar curvature metrics with mean convex boundaries have nontrivial higher homotopy groups.