[permalink] [id link]
Perelman's proof uses a modified version of a Ricci flow program developed by Richard Hamilton.
from
Wikipedia
Some Related Sentences
Perelman's and proof
Several teams of mathematicians have verified that Perelman's proof is correct.
On December 22, 2006, the journal Science honored Perelman's proof of the Poincaré conjecture as the scientific " Breakthrough of the Year ", the first time this had been bestowed in the area of mathematics.
From May to July 2006, several groups presented papers that filled in the details of Perelman's proof of the Poincaré conjecture, as follows:
* Bruce Kleiner and John W. Lott posted a paper on the arXiv in May 2006 which filled in the details of Perelman's proof of the geometrization conjecture.
They initially implied the proof was their own achievement based on the " Hamilton-Perelman theory ", but later retracted the original version of their paper, and posted a revised version, in which they referred to their work as the more modest " exposition of Hamilton – Perelman's proof ".
This last part of the proof appeared in Perelman's third and final paper on the subject.
*: Detailed proof, expanding Perelman's papers.
* Perelman's proof of the Poincaré conjecture: a nonlinear PDE perspective by Terence Tao, unpublished arxiv. org preprint ( written for mathematicians ).
* Lectures on Perelman's proof by T. Tao.
The main difficulty in verifying Perelman's proof of the Geometrization conjecture was a critical use of his Theorem 7. 4 in the preprint ' Ricci Flow with surgery on three-manifolds '.
This method, with full details leading to the proof of Geometrization, can be found in the exposition by B. Kleiner and J. Lott in ' Notes on Perelman's papers ' in the journal Geometry & Topology.
* Bruce Kleiner and John Lott, Notes on Perelman's Papers ( May 2006 ) ( fills in the details of Perelman's proof of the geometrization conjecture ).
1, 57-78 ( expository article explains the eight geometries and geometrization conjecture briefly, and gives an outline of Perelman's proof of the Poincaré conjecture )
" On 22 December 2006, the journal Science recognized Perelman's proof of the Poincaré conjecture as the scientific " Breakthrough of the Year ", the first such recognition in the area of mathematics.
It is the primary tool used in Grigori Perelman's solution of the Poincaré conjecture, as well as in the proof of the Differentiable sphere theorem by Brendle and Schoen.
Perelman's and uses
There is the paper of Shioya and Yamaguchi that uses Perelman's stability theorem and a fibration theorem for Alexandrov spaces.
Perelman's and Ricci
A special case of Perelman's theorems about Ricci flow with surgery is given as follows.
* Bruce Kleiner ( Yale ) and John W. Lott ( University of Michigan ): " Notes & commentary on Perelman's Ricci flow papers ".
Perelman's and by
* Perelman's Song, by Tina S. Chang, listed on Kasman's Mathematical Fiction website, appeared Math Horizons.
Also containing proofs of Perelman's Theorem 7. 4, there is a paper of Morgan and Tian, another paper of Kleiner and Lott, and a paper by Cao and Ge.
Another caricature of Cerf, named Harry Hubris and portrayed by Bert Lahr, appears in Perelman's 1962 play The Beauty Part.
New World faces a major financial slump and the company began to restructure ; first, the Marvel Entertainment Group was sold to financier Ronald Perelman's Andrews Group, in 1989 then New World Entertainment was subsequently acquired by Perelman later in the year.
Perelman's and Richard
* Richard B. Perelman, author of Perelman's Pocket Cyclopedia of Cigars
Perelman's and .
Perelman's work survived review and was confirmed in 2006, leading to his being offered a Fields Medal, which he declined.
All three groups found that the gaps in Perelman's papers were minor and could be filled in using his own techniques.
In 1980, Ronald Perelman, the son of a wealthy Philadelphia businessman, and future " corporate raider " having made several small but successful buyouts, acquired MacAndrews & Forbes, a distributor of licorice extract and chocolate, that Perelman's father had tried and failed to acquire 10 years earlier.
Using the Pantry Pride subsidiary of his holding company, MacAndrews & Forbes Holdings, Perelman's overtures were rebuffed.
After receiving a higher offer from a white knight, private equity firm Forstmann Little & Company, Perelman's Pantry Pride finally was able to make a successful bid for Revlon, valuing the company at $ 2. 7 billion.
Under Perelman's control, Revlon sold 4 divisions: two of which were sold for $ 1 billion, its vision care division was sold for $ 574 million and its National Health Laboratories division was spun out to the public market in 1988.
He lost out at the last minute to Ronald Perelman's slightly higher bid.
There are now several different proofs of Perelman's Theorem 7. 4, or variants of it which are sufficient to prove geometrization.
proof and uses
He uses this as a proof of the existence of atoms:
In this case, if a proof uses this statement, researchers will often look for a new proof that doesn't require the hypothesis ( in the same way that it is desirable that statements in Euclidean geometry be proved using only the axioms of neutral geometry, i. e. no parallel postulate.
Empire magazine praised the film saying " the gaudily gory, virtuoso, hyper-kinetic horror sequel / remake uses every trick in the cinematic book " and confirms that " Bruce Campbell and Raimi are gods " and Caryn James of The New York Times called it " genuine, if bizarre, proof of Sam Raimi's talent and developing skill.
The proof uses Euclid's lemma ( Elements VII, 30 ): if a prime p divides the product of two natural numbers a and b, then p divides a or p divides b ( or perhaps both ).
The proof uses modal logic, which distinguishes between necessary truths and contingent truths.
The proof of Gödel's completeness theorem given by Kurt Gödel in his doctoral dissertation of 1929 ( and a rewritten version of the dissertation, published as an article in 1930 ) is not easy to read today ; it uses concepts and formalism that are outdated and terminology that is often obscure.
George Boolos has since sketched an alternative proof of the first incompleteness theorem that uses Berry's paradox rather than the liar paradox to construct a true but unprovable formula.
The proof of this statement uses the linearity of classical probability, and has exactly the same structure as the proof of the quantum no-cloning theorem.
Newman's proof is arguably the simplest known proof of the theorem, although it is non-elementary in the sense that it uses Cauchy's integral theorem from complex analysis.
The proof uses the classification of finite simple groups.
Although BB84 does not use entanglement, Ekert's protocol uses the violation of a Bell's inequality as a proof of security.
The proof of Euler's identity uses only the formula for the geometric series and the fundamental theorem of arithmetic.
A sig block is easily forged, whereas a digital signature uses cryptographic techniques to provide verifiable proof of authorship.
* Centipede game, the Nash equilibrium of which uses a similar mechanism as its proof.
The alternative is formal software verification, which uses mathematical proof techniques to show the absence of bugs.
An alternative proof uses Prüfer sequences.
While the proof that is a Noetherian ring uses the order structure of, typical proofs in ring theory in general do not assume such additional structure on the ring.
One proof of the impossibility of finding a planar embedding of K < sub > 3, 3 </ sub > uses a case analysis involving the Jordan curve theorem, in which one examines different possibilities for the locations of the vertices with respect to the 4-cycles of the graph and shows that they are all inconsistent with a planar embedding.
The original proof uses hypergeometric functions and innovative tools from the theory of Hilbert spaces of entire functions, largely developed by de Branges.
In logic, a formal proof is not written in a natural language, but instead uses a formal language consisting of certain strings of symbols from a fixed alphabet.
This proof uses definition of even integers, as well as distribution law.
0.163 seconds.