相关论文: A Short Proof of the Poincar\'e Conjecture

In this note we give a detailed proof of a theorem of Aubin.

This paper has been withdrawn by the authors due to crucial error in the main proof (located in Section 2.4). The authors apologize for any inconveniences.

A very short proof of G\"odel's second incompleteness theorem (for set theory, second order arithmetic etc.)

We prove Poincare's Conjecture that every simply connected, closed three-manifold is topologically equivalent to the three-sphere. The proof is founded on the algebraic formulation discovered by J. Stallings.

An analog of Picard's little theorem for entire functions of matrices is proved.

In this paper we prove the WALA conjecture.

We prove Union-Closed sets conjecture.

Recently Z.W.Sun found over hundred conjectured formulas for 1/pi. Many of them were proved by H.H.Chan, J.Wan andW.Zudilin (see [3], [8] in the paper). Here we show that several other formulas in [6] are simple transformations of known…

We do not know whether the main result is true, the proof of theorem 2.1 contains a gap.

We prove new results, related to the Littlewood and Mixed Littlewood conjectures in Diophantine approximation.

In this paper, we prove the conjecture that if there is an odd perfect number, then there are infinitely many of them.

This paper has been withdrawn by the authors due to a mistake in the proof of Theorem 1.

This article is a collected information from some books and papers, and in most cases the original sentences is reserved about twin prime conjecture.

We prove that Ma\~n\'e's conjecture, as stated in {\em Lagrangian flows: the dynamics of globally minimizing orbits}, Bol. Soc. Brasil. Mat. (N.S.) 28 (1997), no. 2, 141--153, contains another conjecture of Ma\~n\'e, stated in {\em Generic…

Here we prove some conjectures on the monotony of combinatorial sequences from the recent preprint of Zhi--Wei Sun.

Using Singular Rescaling We Prove Some Bifurcation Results. This note Presents short proofs for some Bifurcation results which had been appeared with other authors.

A strong form of the Manin-Peyre conjecture with a power saving error term is proved for a certain cubic fourfold.

New cases of the multiplicity conjecture are considered.

It is shown that the Poincar\'e-Birkhoff fixed point theorem may be proven by extending the geometric approach originally devised by Henri Poincar\'e himself, along with several results from elementary differential topology. Beginning with…

We give a simple proof of the Fourier Inversion Theorem, using the methods of nonstandard analysis.