The heat flow on manifolds. Existence and uniqueness of harmonic maps into nonpositively curved image manifolds

Jürgen Jost
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Jürgen Jost: Ruhr-Universität Bochum, Mathematisches Institut

Chapter 3 in Nonlinear Methods in Riemannian and Kählerian Geometry, 1991, pp 87-109 from Springer

Abstract: Abstract In order to warm up, we shall first present the linear case, i.e. look at 3.1.1 % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacq % GHciITcqaHXoqycaGGOaGaamiEaiaacYcacaWG0bGaaiykaaqaaiab % gkGi2kaadshaaaGaeyOeI0IaeuiLdq0aaWbaaSqabeaacqGHsislaa % GccqaHXoqycaGGOaGaamiEaiaacYcacaWG0bGaaiykaiabg2da9iaa % icdaaaa!4A3C! $$\frac{{\partial \alpha (x,t)}}{{\partial t}} - {\Delta ^ - }\alpha (x,t) = 0$$ 3.1.2 % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySdeMaai % ikaiaadIhacaGGSaGaaGimaiaacMcacqGH9aqpcqaHXoqydaWgaaWc % baGaaGimaaqabaGccaGGOaGaamiEaiaacMcaaaa!413E! $$\alpha (x,0) = {\alpha _0}(x)$$ where 0 ≤ t

Keywords: Local Existence; Closed Geodesic; Compact Riemannian Manifold; Christoffel Symbol; Harmonic Form (search for similar items in EconPapers)
Date: 1991
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DOI: 10.1007/978-3-0348-7706-0_3

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