I somewhere read about gradient flows of functionals in a Riemannian manifold. I want to learn about them. A quick google search did not turn up anything useful. So i am looking for references where they study these. Which literature do you recommend for a beginner in riemannian manifolds/gradient flows?
2026-03-26 23:11:44.1774566704
Gradient flow of functional in a riemannian manifold
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Since you used the term "functional" rather than "function," I assume you're interested in the gradient flow of a function on some (infinite-dimensional) space of metrics, or embeddings, or the like. (The word "functional" traditionally refers to a functions whose domain is itself a space of functions.)
Classic examples are the curve-shortening flow, the mean-curvature flow, the Ricci flow. See this Wikipedia article for explanations and more examples.