相关论文: Gunther's proof of Nash's isometric embedding theo…

We extend the recent study of the k-body embedded Gaussian ensembles by Benet et al. (Phys. Rev. Lett. 87 (2001) 101601-1 and Ann. Phys. 292 (2001) 67) and by Asaga et al. (cond-mat/0107363 and cond-mat/ 0107364). We show that central…

We give an elementary and constructive proof for a theorem of de Smit et Lenstra. Note: In version 1, was missing the proof that "completely secant" implies "1-secant"

Given any short immersion from an $n$-dimensional bounded and simply connected domain into $\mathbb{R}^{n+1}$ and any H\"older exponent $\alpha<(1+n^2-n)^{-1}$, we construct a $C^{1, \alpha}$ isometric immersion arbitrarily close in the…

This is an exposition of the theory of differentiable structures on metric measures spaces, in the sense of Cheeger and Keith.

In this note we prove an inequality for t-geometric means that immediately implies the recent results of Audenaert [2] and Hayajneh-Kittaneh [6].

In this paper we prove two theorems. The first one is a structure result that describes the extrinsic geometry of an embedded surface with constant mean curvature (possibly zero) in a homogeneously regular Riemannian three-manifold, in any…

This is a detailed introductory survey of the cohomological dimension theory of compact metric spaces.

We exhibit isomorphisms of Grassmann spaces and their relationship with collineations and embeddings of the underlying projective spaces.

In this paper, we survey some recent results about the asymptotic expansion of Bergman kernel and we give a Bergman kernel proof of Kodaira embedding theorem.

We give an elementary introduction to the theory of supermembranes.

The isometric immersion of two-dimensional Riemannian manifolds or surfaces in the three-dimensional Euclidean space is a fundamental problem in differential geometry. When the Gauss curvature is negative, the isometric immersion problem is…

We prove a coisotropic embedding theorem \`a l\`a Gotay for pre-multisymplectic manifolds.

We prove that the isometric embedding of any metric of differentiability class C1 in E3 exists. We use simplified notation for the given metric, namely geodesic parameters, and level parameters for the embedded surface in E3. Central to our…

In this paper, we first provide a simple variational proof of the existence of Nash equilibrium in Hilbert spaces by using optimality conditions in convex minimization and Schauder's fixed-point theorem. Then applications of convex analysis…

The famous Nash embedding theorem was aimed for in the hope that if Riemannian manifolds could be regarded as Riemannian submanifolds, this would then yield the opportunity to use extrinsic help. However, as late as 1985 (see \cite{G}) this…

Noether's theorem is widely regarded as one of the most elegant results in theoretical physics. The article presents two simple examples that can be used to demonstrate the basic idea behind Noether's theorem, by deriving a relation between…

An easy to implement and powerful method for the solution of 3D scattering problems that can be well described by Helmholtz equation is presented. The matrix algebra used provides excellent stability versus the number of junctions as well…

An elementary approach to the construction of Coxeter group representations is presented.

We present a proof of Moessner's theorem by double induction, using only basic rules of arithmetic. No prerequisite knowledge is assumed. Familiarity with summation is advised.

For any n-dimensional compact Riemannian manifold (M,g), we construct a canonical t-family of isometric embeddings I_{t}: M->R^{q(t)}, with t>0 sufficiently small and q(t)>>t^{-n/2}. This is done by intrinsically perturbing the heat kernel…