4 citations · 16 across the 21 of their papers we have counts for
21 papers
A Frobenius Theorem on Fréchet Manifolds
Kaveh Eftekharinasab
We investigate the integrability of Fréchet tangent distributions on Fréchet manifolds. We introduce the local well-posedness Condition W for split tangent subbundles, which reduce…
A Class of Functionals on the Sequence Space Satisfying the Palais-Smale Condition
Kaveh Eftekharinasab
We introduce a class of functionals on the space of rapidly decreasing sequences , called -functionals, defined as decomposable sums of quadratic and convex terms…
Spray-Invariant Sets in Infinite-Dimensional Manifolds
Kaveh Eftekharinasab
We introduce the concept of spray-invariant sets on infinite-dimensional manifolds, where any geodesic of a spray starting in the set stays within it for its entire domain. These s…
Global Implicit Function Theorems and Critical Point Theory in Fréchet Spaces
Kaveh Eftekharinasab
We prove two versions of a global implicit function theorem, which involve no loss of derivative, for Keller's -mappings between arbitrary Fréchet spaces. Subsequently, wi…
Geometry Via Sprays on Frechet Manifolds
Kaveh Eftekharinasab
We construct connection maps and linear symmetric connections on tangent and second-order tangent bundles for \fr manifolds using the notion of a spray. For these manifolds, we cha…
Multiplicity Theorems for Frechet Manifolds
Kaveh Eftekharinasab
We prove multiplicity theorems for Keller -functionals on Frechet spaces and Finsler manifolds which are invariant under the action of a discrete subgroup. For such functi…
Some critical point results for Fréchet manifolds
Kaveh Eftekharinasab
We prove a so-called linking theorem and some of its corollaries, namely a mountain pass theorem and a three critical points theorem for Keller -functional on - Freche…
Some applications of transversality for infinite dimensional manifolds
Kaveh Eftekharinasab
We present some transversality results for a category of Fréchet manifolds, the so-called -Fréchet manifolds. In this context, we apply the obtained transversality results to…
Finslerian geodesics on Fréchet manifolds
Kaveh Eftekharinasab, Valentyna Petrusenko
We establish a framework, namely, nuclear bounded Fréchet manifolds endowed with Riemann-Finsler structures to study geodesic curves on certain infinite dimensional manifolds such…
A Global Diffeomorphism Theorem for Fréchet spaces
Kaveh Eftekharinasab
We give sufficient conditions for a -local diffeomorphism between Fréchet spaces to be a global one. We extend the Clarke's theory of generalized gradients to the more gen…
On the generalization of the Darboux theorem
Kaveh Eftekharinasab
We provide sufficient conditions for the existence of Darboux charts on weakly symplectic bounded Fréchet manifolds by using the Moser's trick.
On the existence of a global diffeomorphism between Fréchet spaces
Kaveh Eftekharinasab
We provide sufficient conditions for the existence of a global diffeomorphism between tame Fréchet spaces. We prove a version of the Mountain Pass Theorem which is a key ingredient…
A simple proof of the short-time existence and uniqueness for Ricci flow
Kaveh Eftekharinasab
In this short note, we give simple proof of the Ricci flow's local existence and uniqueness on closed Einstein manifolds. We suggest a new setting for studying the space of Riemann…
Transversality and Lipschitz-Fredholm maps
Kaveh Eftekharinasab
We study transversality for Lipschitz-Fredholm maps in the context of bounded Fréchet manifolds. We show that the set of all Lipschitz-Fredholm maps of a fixed index between Fréche…
Fréchet Lie algebroids and their cohomology
Kaveh Eftekharinasab
We define Lie and Courant algebroids on Fréchet manifolds. Moreover, we construct a Dirac structure on the generalized tangent bundle of a Fréchet manifold and show that it inherit…
A Generalized Palais-Smale Condition in the Fréchet space setting
Kaveh Eftekharinasab
We extend the Palais-Smale condition to Keller's -functionals on Fréchet spaces. Using this condition together with Ekeland's variational principle, we obtain some results r…
The Morse-Sard-Brown Theorem for Functionals on Bounded-Fréchet-Finsler Manifolds
Kaveh Eftekharinasab
In this paper, we study Lipschitz-Fredholm vector fields on Bounded-Fréchet-Finsler manifolds. In this context we generalize the Morse-Sard-Brown theorem, asserting that if is…
Geometry of Bounded Frechet Manifolds
Kaveh Eftekharinasab
In this paper we develop the geometry of bounded Fréchet manifolds. We prove that a bounded Fréchet tangent bundle admits a vector bundle structure. But the second order tangent bu…
A note on Gaussian curvature of harmonic surfaces
Kaveh Eftekharinasab
It was proved that the fundamental group of the space of harmonic polynomials of degree , with the same Gaussian curvature is not trivial. Furthermore, we give an exam…
Sard's theorem for mappings between Fréchet manifolds
Kaveh Eftekharinasab
In this paper we prove an infinite-dimensional version of Sard's theorem for Fréchet manifolds. Let and be bounded Fréchet manifolds such that the topologies of their m…
Curvature forms and Curvature functions for 2-manifolds with boundary
Kaveh Eftekharinasab
We obtained that any 2-form and any smooth function on 2-manifolds with boundary can be realized as the curvature form and the gaussian curvature function of some Riemmanian metric…