Abstract
As we briefly discussed in the introduction, the notion of gradient flows in a metric space relies on two elementary but basic concepts: the metric derivative of an absolutely continuous curve with values in and the upper gradients of a functional defined in . The related definitions are presented in the next two sections (a more detailed treatment of this topic can be found for instance in [20]); the last one deals with curves of maximal slope.
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© 2008 Birkhäuser Verlag AG
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(2008). Curves and Gradients in Metric Spaces. In: Gradient Flows. Lectures in Mathematics ETH Zürich. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8722-8_3
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DOI: https://doi.org/10.1007/978-3-7643-8722-8_3
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-8721-1
Online ISBN: 978-3-7643-8722-8
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