TL;DR
This paper provides an overview of Ricci flow theory, proves the Poincaré conjecture, and offers a complete proof of the Calabi-Yau conjecture, contributing significantly to geometric analysis.
Contribution
It presents a comprehensive proof of the Calabi-Yau conjecture, along with an educational exposition of Ricci flow and alternative proofs of the Poincaré conjecture.
Findings
Proof of the Poincaré conjecture via Ricci flow
Complete proof of the Calabi-Yau conjecture
Educational exposition of elliptization and Ricci flow
Abstract
This memoire consists of two main results. In the first one we describe Ricci flow theory and we give an educative way for proving Elliptization Conjecture and then we prove Poincare conjecture which is the second proof of Perelman for Poincare conjecture. In the second one which is the main propose of our memoire, we exhibit a complete proof of Calabi-Yau conjecture.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Algebraic Geometry and Number Theory