Riemannian center of mass and mollifier smoothing
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Publication:4125498
DOI10.1002/cpa.3160300502zbMath0354.57005OpenAlexW2109409043WikidataQ115406205 ScholiaQ115406205MaRDI QIDQ4125498
Publication date: 1977
Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1002/cpa.3160300502
Groups acting on specific manifolds (57S25) Compact Lie groups of differentiable transformations (57S15) Global Riemannian geometry, including pinching (53C20) Differential inequalities involving functions of a single real variable (34A40) Manifolds of mappings (58D15)
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Cites Work