Related papers: Harder-Narasimhan theory

It is shown that any singular Lagrangian theory: 1) can be formulated without the use of constraints by introducing a Clairaut-type version of the Hamiltonian formalism; 2) leads to a special kind of nonabelian gauge theory which is similar…

The paper presents a counterexample to the Hodge conjecture.

We prove some injectivity, torsion-free, and vanishing theorems for simple normal crossing pairs. Our results heavily depend on the theory of mixed Hodge structures on compact support cohomology groups. We also treat several basic…

We give a new proof of an important theorem by Nakazi using recent results by Sarason in his seminal paper on agebraic properties of truncated Toeplitz operators.

Herbrand's Theorem is a fundamental result in mathematical logic which provides a reduction of first-order formulas satisfied by a universal class to formulas free of existential quantifiers. In this work, a simpler and self-contained…

In this paper we give a rigorous proof of the equivalence of some different forms of Faraday's law of induction clarifying some misconceptions on the subject and emphasizing that many derivations of this law appearing in textbooks and…

We give a proof of Fermat's little theorem which does not use nor arithmetic(Euclidean algorithm) neither algebra (group theory), but it rather employs the field of the formal power series Q((x)). The note is an example of a mathematical…

In this largely expository article, we present a Kawamata-Viehweg type formulation of the (logarithmic) Akizuki-Nakano Vanishing Theorem. While the result is likely known to the experts, it does not seem to appear in the existing…

We will prove the Brannan conjecture for particular values of the parameter. The basic tool of the study is an integral representation published in a recent work [3].

We consider the generalized Egorov's statement (Egorov's Theorem without the assumption on measurability of the functions, see \cite{tw:nget}) in the case of an ideal convergence and a number of different types of ideal convergence notion.…

Our main theorem is an extension of the well-known Mizoguchi-Takahaashi's fixed point theorem [N. Mizogochi and W. Takahashi, Fixed point theorems for multi-valued mappings on complete metric space, {\it J. Math. Anal. Appl.} 141 (1989)…

In this paper under some conditions we generalize a theorem of Harish-Chandra concerning representability of Fourier transforms of orbital integrals.

In 2012, Nazarov used Bergman kernels and Hormander's $L^2$ estimates for the $\bar\partial$-equation to give a new proof of the Bourgain--Milman theorem for symmetric convex bodies and made some suggestions on how his proof should extend…

We define what we call morphisms of Cartan connections. We generalize the main theorems on Cartan connections to theorems on morphisms. Many of the known constructions involving Cartan connections turn out to be examples of morphisms. We…

A proof for the original Riemann hypothesis is proposed based on the infinite Hadamard product representation for the Riemann zeta function and later generalized to Dirichlet L-functions. The extension of the hypothesis to other functions…

We study the question of generalizing light-front field theories to finite temperature. We show that the naive generalization has serious problems and we identify the source of the difficulty. We provide a proper generalization of these…

The article provides a modest survey of the absolute theory of general systems of (partial) differential equations. The equations are relieved of all additional structures and subject to quite arbitrary change of the variables. An abstract…

We prove a logarithmic convexity result for exponentially weighted $L^2$-norms of solutions to electromagnetic Schr\"odinger equation, without needing to assume smallness of the magnetic potential. As a consequence, we can prove a unique…

In this paper we give a complete proof of the Brumer-Stark conjecture over $\mathbf{Z}$.

We consider the implications of some simple assumptions about the nature of the quantum theory of gravity which are plausible for a class of possible theories I have been attempting to construct. The simple assumptions turn out to have…