Geodesic
Nonnegative Scalar Curvature and Area Decreasing Maps
Symmetry, integrability and geometry: methods and applications, Tome 16 (2020) Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $\big(M,g^{TM}\big)$ be a noncompact complete spin Riemannian manifold of even dimension $n$, with $k^{TM}$ denote the associated scalar curvature. Let $f\colon M\rightarrow S^{n}(1)$ be a smooth area decreasing map, which is locally constant near infinity and of nonzero degree. We show that if $k^{TM}\geq n(n-1)$ on the support of ${\rm d}f$, then $ \inf \big(k^{TM}\big)0$. This answers a question of Gromov. We use a simple deformation of the Dirac operator to prove the result. The odd dimensional analogue is also presented.
Keywords: scalar curvature, spin manifold, area decreasing map. 
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     author = {Weiping Zhang},
     title = {Nonnegative {Scalar} {Curvature} and {Area} {Decreasing} {Maps}},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2020_16_a32/}
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Weiping Zhang. Nonnegative Scalar Curvature and Area Decreasing Maps. Symmetry, integrability and geometry: methods and applications, Tome 16 (2020). http://geodesic.mathdoc.fr/item/SIGMA_2020_16_a32/

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