### 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 language | English (US) |
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Title of host publication | Foundations of Mathematics and Physics One Century After Hilbert |

Subtitle of host publication | New Perspectives |

Publisher | Springer International Publishing |

Pages | 135-158 |

Number of pages | 24 |

ISBN (Electronic) | 9783319648132 |

ISBN (Print) | 9783319648125 |

DOIs | |

State | Published - May 26 2018 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Mathematics(all)

### Cite this

*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

**A dozen problems, questions and conjectures about positive scalar curvature.** / Gromov, Mikhael.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Foundations of Mathematics and Physics One Century After Hilbert: New Perspectives.*Springer International Publishing, pp. 135-158. https://doi.org/10.1007/978-3-319-64813-2_6

}

TY - CHAP

T1 - A dozen problems, questions and conjectures about positive scalar curvature

AU - Gromov, Mikhael

PY - 2018/5/26

Y1 - 2018/5/26

N2 - 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.

AB - 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.

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U2 - 10.1007/978-3-319-64813-2_6

DO - 10.1007/978-3-319-64813-2_6

M3 - Chapter

SN - 9783319648125

SP - 135

EP - 158

BT - Foundations of Mathematics and Physics One Century After Hilbert

PB - Springer International Publishing

ER -