Nonnegative Scalar Curvature and Area Decreasing Maps

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2020
• Main Author: Zhang, Weiping
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2020
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/210717
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: 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...