相关论文: Collar lemma for Hitchin representations

Given a Riemann surface $X = (\Sigma, J)$ we find an expression for the dominant term for the asymptotics of the holonomy of opers over that Riemann surface corresponding to rays in the Hitchin base of the form $(0,0,\cdots,t\omega_n)$.…

Given a convex representation $\rho:\Gamma\to\textrm{PGL}(d,\mathbb{R})$ of a convex co-compact group $\Gamma$ of $\mathbb{H}^k$ we find upper bounds for the quantity $\alpha h_\rho,$ where $h_\rho$ is the entropy of $\rho$ and $\alpha$ is…

An argument is provided for the equality case of the high dimensional Bonnesen inequality for sections. The known equality case of the Bonnesen inequality for projections is presented as a consequence.

The paper studies possible functional analogs of classical problems from convex geometry. In particular, we provide some bounds in the functional Shephard, Busemann-Petty, and Milman problems generalizing known bounds in this problems for…

A classical analogue of the Adlam-Kent "Quantum paradox of choice" (arXiv:1509.04226) is presented.

We are concerned with the Dirichlet problem for a class of Hessian type equations. Applying some new methods we are able to establish the $C^2$ estimates for an approximating problem under essentially optimal structure conditions. Based on…

We prove the finiteness of log pluricanonical representations for projective log canonical pairs with semi-ample log canonical divisor. As a corollary, we obtain that the log canonical divisor of a projective semi log canonical pair is…

Some occurrences of $n$ can be replaced by $n-1$ in a special case of the Shapley-Folkman lemma.

We try to apply a known equivalence, for RH about Riemann Z function, to Dirichlet L functions with primitive characters. The aim is to give a small contribution to the proof of the generalized version of Riemann Hypothesis (RH).

We prove that Leibniz homology of Lie algebras can be described as functor homology in the category of linear functors from a category associated to the Lie operad.

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].

In the category of Hom-Leibniz algebras we introduce the notion of representation as adequate coefficients to construct the chain complex to compute the Leibniz homology of Hom-Leibniz algebras. We study universal central extensions of…

The Gerstenhaber and Schack cohomology comparison theorem asserts that there is a cochain equivalence between the Hochschild complex of a certain algebra and the usual singular cochain complex of a space. We show that this comparison…

The Hitchin component is a connected component of the character variety of reductive group homomorphisms from the fundamental group of a closed surface S of genus greater than 1 to the Lie group PSL_m(R). The Teichmuller space of S…

We propose a reflection principle for holomorphic objects in ${\Bbb C}^n$. Our construction generalizes the classical principle of H.Lewy, S.Pinchuk and S.Webster.

Covering theory is an important tool in representation theory of algebras, however, the results and the proofs are scattered in the literature. We give an introduction to covering theory at a level as elementary as possible.

We state the analogs of Kontsevich's formality conjecture for Hochschild and cyclic chains, as well as their

We establish a necessary and sufficient condition for a representation of a lattice ordered semigroup to be regular, in the sense that certain extensions are completely positive definite. This result generalizes a theorem due to Brehmer…

We give a purely derivator-theoretical reformulation and proof of a classic result of Happel and Ladkani, showing that it occurs uniformly across stable derivators and it is then independent of coefficients. The resulting equivalence…

We derive a piecewise-linear formula for the rigid representation of a Dynkin quiver of a given dimension vector, and illustrate the formula in several examples.