Perelman's proof of the Poincaré conjecture: a nonlinear PDE perspective

Abstract

We discuss some of the key ideas of Perelman's proof of Poincaré's conjecture via the Hamilton program of using the Ricci flow, from the perspective of the modern theory of nonlinear partial differential equations.

arXiv comment42 pages, unpublished

References in corpus (4)

• Ricci flow with surgery on three-manifolds
• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds
• Ricci Flow and the Poincare Conjecture
• A geometric interpretation of Hamilton's Harnack inequality for the Ricci flow

Cited by in corpus (6)

• Five types of blow-up in a semilinear fourth-order reaction-diffusion equation: an analytic-numerical approach
• Minimally invasive surgery for Ricci flow singularities
• A Homotopy-like Class Invariant for Sub-manifolds of Punctured Euclidean Spaces
• The method of the kernel of the evolution equation in the theory of gravity
• Perelman's collapsing theorem for 3-manifolds
• Perelman's functional and reduced volume