Dynamics of Steady Euler Flows: New Results

Related lectures (30)

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Introduces retractions and vector fields on manifolds, providing examples and discussing smoothness and extension properties.

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Covers optimization on manifolds, focusing on smooth manifolds and functions, and the process of gradient descent.

Covers the definition of retraction, open submanifolds, local defining functions, tangent spaces, and Riemannian metrics.

Covers connections on manifolds, symmetric connections, Lie brackets, and compatibility with the metric in Riemannian geometry.

Covers Hessians, symmetry, and examples related to vector fields, functions, and manifolds.

Covers optimization on manifolds, smoothness, tools needed for optimization, and advanced algorithms using Hessians and Riemannian connections.

Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.

Delves into topological entropy in compact manifolds and Reeb flows, emphasizing the forcing of entropy via cylindrical contact homology.

Explores Riemannian metrics on manifolds and the concept of Riemannian submanifolds in Euclidean spaces.