Related papers: Vector variational principle
In this paper we show an index theorem for gerbes
A simple proof of the convergence of the variational regularization, with the regularization parameter, chosen by the discrepancy principle, is given for linear operators under suitable assumptions. It is shown that the discrepancy…
The article presents the proof of Casas-Alvero conjecture.
We prove existence of an invariant measure on a hypergroup.
We survey some recent progress in the theory of vector bundles on algebraic varieties and related questions in algebraic K-theory.
A surprising simple result about quadrilaterals is given as an application of the vector triple product identity.
We present a proof of Hadamard Inverse Function Theorem by the methods of Variational Analysis, adapting an idea of I. Ekeland and E. Sere.
A method for designing variational principles for the dynamics of a possibly dissipative and non-conservatively forced chain of particles is demonstrated. Some qualitative features of the formulation are discussed.
We prove a weak version of a bigness criterion for equivariant vector bundles on toric varieties.
This paper gives a new elementary proof of the theorem that all vector bundles on $\mathbb P^1$ split into the direct sum of line bundles. The proof is based on the study of divisors associated to germs of sections at the generic point.
In this paper, we prove a semistable reduction type theorem for multi-filtered vector spaces (or known as multi-weighted vector spaces).
We prove a new vanishing theorem generalizing that of Le Potier for Schur functors of a vector bundle.
We prove a uniformization theorem in complex algebraic geometry.
We find an elementary proof for Voiculescu's theorem on the polar decomposition of circular variables.
We prove a uniqueness theorem for an entire function, which shares certain values with its higher order derivatives.
We present a relative form of the Toponogov comparison theorem.
We present a new, elementary, dynamical proof of the prime number theorem.
A multivariate Gauss-Lucas theorem is proved, sharpening and generalizing previous results on this topic. The theorem is stated in terms of a seemingly new notion of convexity. Applications to multivariate stable polynomials are given.
We prove Union-Closed sets conjecture.
We give an abstract approach to the results of Adams and Nobel, [1]. It allows to exhibit a new property of VC classes. It should be stressed that the basic ideas of proofs can be found in [1].