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dc.contributor.authorBär, Christian
dc.contributor.authorHanke, Bernhard
dc.date.accessioned2021-01-04T15:06:43Z
dc.date.available2021-01-04T15:06:43Z
dc.date.issued2021-01-04
dc.identifier.urihttp://publications.mfo.de/handle/mfo/3824
dc.description.abstractBased 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.en_US
dc.language.isoen_USen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2021-01
dc.subjectManifolds with boundaryen_US
dc.subjectLower scalar curvature boundsen_US
dc.subjectLower mean curvature boundsen_US
dc.subjectAtiyah-Patodi-Singer index formulaen_US
dc.subjectInfinite K-areaen_US
dc.subjectArea-enlargeabilityen_US
dc.subjectDeformations of Riemannian metricsen_US
dc.subjectMin-Oo conjectureen_US
dc.subjectSpaces of positive scalar curvature metrics with conditions on the second fundamental form of the boundaryen_US
dc.titleBoundary Conditions for Scalar Curvatureen_US
dc.typePreprinten_US
dc.rights.licenseDieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.de
dc.rights.licenseThis document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.en
dc.identifier.doi10.14760/OWP-2021-01
local.scientificprogramResearch in Pairs 2020en_US
local.series.idOWP-2021-01en_US
local.subject.msc53en_US
local.subject.msc58en_US
dc.identifier.urnurn:nbn:de:101:1-2021020215292937559473
dc.identifier.ppn1747393517


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