Nonnegative Scalar Curvature and Area Decreasing Maps

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2020
• 1. Verfasser: Zhang, Weiping
• Format: Artikel
• Sprache: English
• Veröffentlicht: Інститут математики НАН України 2020
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/210717
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: Nonnegative Scalar Curvature and Area Decreasing Maps. Weiping Zhang. SIGMA 16 (2020), 033, 7 pages

Let (M, gᵀᴹ) be a noncompact complete spin Riemannian manifold of even dimension n, with kᵀᴹ denoting the associated scalar curvature. Let 𝑓: M → Sⁿ(1) be a smooth area decreasing map, which is locally constant near infinity and of nonzero degree. We show that if kᵀᴹ ≥ n(n−1) on the support of d𝑓, t...