Geometric quantization of complex Monge-Ampère Operator for certain diffusion flows

Julien Keller (1)

1 I2M - Institut de Mathématiques de Marseille

Certain natural geometric evolution flows for Kahler metrics have been interpreted as anisotropic filtering operators. These flows are typically given by highly non linear PDE and involve usually transcendental and non-constructive techniques. The main objective of this note is to show that in certain cases, Geometric Quantization theory helps to overcome these difficulties and provides new algorithms based on S.K. Donaldson’s ideas.

Mots clés: Donaldson; balanced; Fischer metric; Rao; statistical model; diffusion flows

Domaines: Géométrie différentielle [math.DG]; Variables complexes [math.CV]; Géométrie algorithmique [cs.CG]

Julien Keller. Geometric quantization of complex Monge-Ampère Operator for certain diffusion flows. Geometric Science of Information, First International Conference, GSI 2013, Paris, France,, Aug 2016, Paris, France. ⟨10.1007/978-3-642-40020-9⟩. ⟨hal-01282555⟩