Related papers: Proofs On Arnold Chord Conjecture And Weinstein Co…
In this article, we give proofs on the Arnold Lagrangian intersection conjecture on the cotangent bundles, Arnold-Givental Lagrangian intersection conjecture and the Arnold fixed point conjecture.
We prove the Arnold chord conjecture on cotangent bundles of open manifold by Gromov's nonlinear Fredholm alternative for $J-$holomorphic curves.
The present paper is a continuation of the study of the interplay between the contact Hamiltonian dynamics and the moduli theory of (perturbed) contact instantons and its applications initiated in [Oh21b, Oh22a]. In this paper we prove…
In this article, we give a proof on the Arnold-Chekanov Lagrangian intersection conjecture on the cotangent bundles and its generalizations.
We give an proof on the Weinstein conjecture on the cotangent bundles of open manifolds. Its proof is based on Gromov's nonlinear Fredholm alternative.
Let $ R \subset \R $ be a GCD-domain. In this paper, Weinberg's conjecture on the $ n \times n $ matrix algebra $ M_{n}(R) \ (n \geq 2) $ is proved. Moreover, all the lattice orders (up to isomorphisms) on a full $ 2 \times 2 $ matrix…
In this paper, we survey some recent results on the Artin conjecture and discuss some aspects for the Artin conjecture.
We provide a proof of the Borwein Conjecture using analytic methods.
In this note we prove the Weinstein conjecture for a class of symplectic manifolds including the uniruled manifolds based on Liu-Tian's result.
We establish a version of the Arnold conjecture, both the degenerate and non-degenerate case, for target manifolds equipped with Clifford pencils of symplectic structures and the domains (time-manifolds) equipped with frames of…
Using algebraic transformations and equivalent reformulations we derive a number of new results from some earlier ones (by the author) in more accepted terms closely related to well-known conjectures of Bondy and Jung including a number of…
In [R2] and [RO] the Arnold conjecture for closed symplectic manifolds with trivial second homotopy group was proved. This proof used surgery and cobordism theory. Here we give a purely cohomological proof of this result.
New cases of the multiplicity conjecture are considered.
This is an introduction to Taubes's proof of the Weinstein conjecture, written for the AMS Current Events Bulletin. It is intended to be accessible to nonspecialists, so much of the article is devoted to background and context.
An technically interesting proof of a known theorem.
We prove (a weak version of) Arnold's Chord Conjecture using Gromov's ``classical'' idea in to produce holomorphic disks with boundary on a Lagrangian submanifold.
In this paper we give a complete proof of the Brumer-Stark conjecture over $\mathbf{Z}$.
In the 1960s Arnold conjectured that a Hamiltonian diffeomorphism of a closed connected symplectic manifold $(M,\omega)$ should have at least as many contractible fixed points as a smooth function on $M$ has critical points. Such a…
We give a detailed proof of the homological Arnold conjecture for nondegenerate periodic Hamiltonians on general closed symplectic manifolds $M$ via a direct Piunikhin-Salamon-Schwarz morphism. Our constructions are based on a coherent…
The existence of a "Plastikstufe" for a contact structure implies the Weinstein conjecture for all supporting contact forms.