A dozen problems, questions and conjectures about positive scalar curvature

Misha Gromov

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

Unlike manifolds with positive sectional and with positive Ricci curvatures which aggregate to modest (roughly) convex islands in the vastness of all Riemannian spaces, the domain {SC > 0} of manifolds with positive scalar curvatures protrudes in all direction as a gigantic octopus or an enormous multi-branched tree. Yet, there are certain rules to the shape of {SC > 0} which limit the spread of this domain but most of these rules remain a guesswork. In the present paper we collect a few "guesses" extracted from a longer article, which is still in preparation: 100 Questions, Problems and Conjectures around Scalar Curvature. Some of these "guesses" are presented as questions and some as conjectures. Our formulation of these conjectures is not supposed to be either most general or most plausible, but rather maximally thought provoking.

Original languageEnglish (US)
Title of host publicationFoundations of Mathematics and Physics One Century After Hilbert
Subtitle of host publicationNew Perspectives
PublisherSpringer International Publishing
Pages135-158
Number of pages24
ISBN (Electronic)9783319648132
ISBN (Print)9783319648125
DOIs
StatePublished - May 26 2018

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Mathematics(all)

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  • Cite this

    Gromov, M. (2018). A dozen problems, questions and conjectures about positive scalar curvature. In Foundations of Mathematics and Physics One Century After Hilbert: New Perspectives (pp. 135-158). Springer International Publishing. https://doi.org/10.1007/978-3-319-64813-2_6