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ISBN: 0821835157 9780821835159 Year: 2004 Publisher: Providence (R.I.): American mathematical society,
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Global differential geometry. --- Ricci flow. --- Riemannian manifolds.
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ISBN: 9781470428402 1470428407 Year: 2018 Publisher: Providence, RI : American Mathematical Society,
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Evolution equations --- Asymptotic expansions. --- Curvature. --- Singularities (Mathematics) --- Équations d'évolution --- Développements asymptotiques. --- Courbure. --- Singularités (mathématiques) --- Asymptotic theory. --- Théorie asymptotique. --- Asymptotic expansions --- Curvature --- Asymptotic developments --- Asymptotic theory in evolution equations --- Asymptotic theory --- Développements asymptotiques --- Courbure --- Singularités (Mathématiques) --- Théorie asymptotique --- Geometry, Algebraic --- Calculus --- Curves --- Surfaces --- Asymptotes --- Convergence --- Difference equations --- Divergent series --- Functions --- Numerical analysis
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ISBN: 1470444151 Year: 2018 Publisher: Providence, Rhode Island : American Mathematical Society,
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The authors study noncompact surfaces evolving by mean curvature flow (mcf). For an open set of initial data that are C^3-close to round, but without assuming rotational symmetry or positive mean curvature, the authors show that mcf solutions become singular in finite time by forming neckpinches, and they obtain detailed asymptotics of that singularity formation. The results show in a precise way that mcf solutions become asymptotically rotationally symmetric near a neckpinch singularity.
Evolution equations --- Asymptotic expansions. --- Curvature. --- Singularities (Mathematics) --- Asymptotic theory.
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