Filling radius, quantitative K-theory and positive scalar curvature

Wang, Jinmin; Xie, Zhizhang; Yu, Guoliang; Zhu, Bo

doi:10.2140/gt.2026.30.2961

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ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

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Filling radius, quantitative $K$-theory and positive scalar curvature

Jinmin Wang, Zhizhang Xie, Guoliang Yu and Bo Zhu

Geometry & Topology 30 (2026) 2961–2992

DOI: 10.2140/gt.2026.30.2961

Abstract

We prove a quantitative upper bound on the filling radius of complete, spin manifolds with uniformly positive scalar curvature using the quantitative operator $K$ -theory and index theory.

Keywords

scalar curvature, filling radius, quantitative K-theory, Dirac operator

Mathematical Subject Classification

Primary: 53C23, 19D55

Secondary: 58B34, 46L80

References

Publication

Received: 1 March 2024

Revised: 7 April 2026

Accepted: 8 May 2026

Published: 30 August 2026

Proposed: Bruce Kleiner

Seconded: David Fisher, Martin R Bridson

Authors

Jinmin Wang
Institute of Mathematics Chinese Academy of Sciences Beijing China

Zhizhang Xie
Department of Mathematics Texas A&M University College Station, TX United States

Guoliang Yu
Department of Mathematics Texas A&M University College Station, TX United States

Bo Zhu
Yau Mathematical Sciences Center Tsinghua University Beijing China

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Volume 30, issue 8 (2026)