All Questions
Tagged with gradient-flows riemannian-geometry
7 questions
3
votes
1
answer
162
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Gradient flows: evolution of geodesics
I’m trying to understand if, when I move the marginals of a Wasserstein geodesic along a contractive flow, the geodesic between the new probability measures is “near” to the geodesic
connecting the ...
- 33
1
vote
1
answer
181
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Gradient descent under the presence of symmetries
Let $M$ be a Riemannian manifold (I'm happy to assume it is Euclidean space) with a function $f: M \to \mathbb R$ and a group of isometries $G$ acting on $M$ and preserving $f$, i.e., $f(gm) = f(m)$ ...
- 7,746
1
vote
0
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154
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Relation between two gradient dynamics
If $f:\mathbb{R}^n\rightarrow\mathbb{R}_+$ is a nonnegative real analytic function and $g:\mathbb{R}^n\rightarrow\mathbb{R}$ is a strongly convex smooth function with a surjective gradient $\nabla g:\...
- 311
0
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0
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254
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Geodesics and gradient flow
Is there a construction in Riemannian geometry which relates the gradient flow of a function on a manifold with a certain metric with geodesics on another related manifold with its own metric?
- 41
6
votes
1
answer
259
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Intersection of self-shrinkers
I have a problem regarding a statement in the paper Smooth compactness of self-shrinkers by Colding and Minicozzi.
In the article, they define a surface $\Sigma$ in $\mathbb R^3$ to be a self-shrinker ...
- 402
0
votes
0
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152
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Metric obstructions for area-preserving diffeomorphisms with constant singular values
Let $\mathbb{T}^2$ be the topological $2$-dimensional torus, and let $0<\sigma_1 < \sigma_2$ satisfy $\sigma_1 \sigma_2=1$. Let $g$ be an arbitrary smooth Riemannian metric on $\mathbb{T}^2$.
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- 6,741
1
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0
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259
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Expressing the Ricci flow as a gradient flow in a case that manifold $(M,g)$ is a Riemannian manifold with boundary
I want to express the Ricci flow as a gradient flow in a case that manifold $(M,g)$ is a Riemannian manifold with boundary. For this I use the Einstein-Hilbert action
$$S(g_{\mu \nu})=\frac{1}{16\pi}\...
- 1,303