It is defined as for a Riemannian matric, there is a unique solution to the "evolution" equation for a smooth metric on a closed manifold over a very short duration, analogous to the process of diffusion of heat. It was put into the frame by Richard Hamilton in 1981 on the basis of the geometrization conjecture of Thurston. It was later modified by the Russian scientist Grigori Perelman to introduce the concept of "Ricci Flow With Surgery". He used it to provide a solution of the Poincare conjecture, a problem that stood out unsolved for a century! Also, it was the tool used to prove the Differential sphere theorem.
Now-a-days, there's an uprise of interest to study how multi-dimensional Riemannian manifolds evolve under it and how it forms singularities. The concept is indeed a product of the enormous development of mathematical analysis and it can be utilized by different forms like the exponential isothermal co-ordinate chart form or the cigar soliton solution. Obviously the mathematicians in the future will use and develop this powerful tool to gain a brighter insight of how the Universe actually is and works!
Now-a-days, there's an uprise of interest to study how multi-dimensional Riemannian manifolds evolve under it and how it forms singularities. The concept is indeed a product of the enormous development of mathematical analysis and it can be utilized by different forms like the exponential isothermal co-ordinate chart form or the cigar soliton solution. Obviously the mathematicians in the future will use and develop this powerful tool to gain a brighter insight of how the Universe actually is and works!
