Gradient flow of the norm squared of a moment map

By Eugene Lerman. 2004

62 citations recorded by the source corpus.

We present a proof due to Duistermaat that the gradient flow of the norm squared of the moment map defines a deformation retract of the appropriate piece of the manifold onto the zero level set of the moment map. Duistermaat's proof is an adaptation of Lojasiewicz's argument for analytic functions to functions which are locally analytic.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/fbbc8d7ef6cb2328a17421ccebd64542c46cc300

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Song Sun
2. Xiuxiong Chen
3. G'abor Sz'ekelyhidi
4. Robert J. Berman
5. Gregory D. Landweber
6. Megumi Harada
7. Chi Li
8. R. Dervan

In Mathematical Physics

1. Song Sun
2. Xiuxiong Chen
3. Gregory D. Landweber
4. Megumi Harada
5. G'abor Sz'ekelyhidi
6. Robert J. Berman
7. B. Weinkove
8. Jingrui Cheng

Citations in the corpus

• Calabi flow, Geodesic rays, and uniqueness of constant scalar curvature K\ (2010, background): “As we will see more explicitly later, a theorem of Duistermaat [33] says that for x(0) close to a zero of µ, the flow x(t) converges polynomially fast to a limit in µ−1(0).”
• Surjectivity for Hamiltonian G-spaces in K-theory (2005, background): “(This result is due to an unpublished manuscript of Duistermaat, whose argument is reproduced in [28].”