We prove that the only complex parabolic geometries on Calabi–Yau manifolds are the homogeneous geometries on complex tori. We also classify the complex parabolic geometries on homogeneous compact Kähler manifolds.

Given an automorphism τ of a smooth complex algebraic curve X, there is an induced action on the moduli space M of semi-stable rank 2 holomorphic bundles with fixed determinant. We give a complete description of the fixed variety in terms of moduli spaces of parabolic bundles on the quotient curve X/〈τ〉.

In this paper, we study the solvmanifolds constructed from any parabolic subalgebras of any semisimple Lie algebras. These solvmanifolds are naturally homogeneous submanifolds of symmetric spaces of noncompact type. We show that the Ricci curvatures of our solvmanifolds coincide with the restrictions of the Ricci curvatures of the ambient symmetric spaces. Consequently, all of our solvmanifolds...

In this article, we study the parabolic equation ∂tu−c(t)∂ xu = f in the non-necessarily rectangular domain Ω = {(t, x) ∈ R : 0 < t < T, φ1(t) < x < φ2(t)}. The boundary conditions are of Robin type, while the right-hand side lies in the Lebesgue space L2(Ω). Our aim is to find conditions on c and the functions (φi)i=1,2 such that the solution belongs to the anisotropic Sobolev space H1,2(Ω) = ...

We study asymptotic proximity as t ! 1 of the solutions of the inverse problem for a pseudo-parabolic equation with an unknown source function. The overdetermination condition is given in integral form. 2003 Elsevier Inc. All rights reserved.

Department of Physiology, Nagoya University Graduate School of Medicine, Nagoya 466–8550, Japan (M.T., T.F., M.S., H.T.); International Cooperative Research Project/Solution-Oriented Research for Science and Technology, Cell Mechanosensing Project, Japan Science and Technology Agency, Nagoya 466–8550, Japan (M.S.); and Department of Molecular Physiology, National Institute for Physiological Sci...

In this paper, we address the following initial value problem

Given an element w of a Coxeter group, let ai(w) be the number of elements less than w in Bruhat order. A theorem of Björner and Ekedahl states that if W is crystallographic, then ai(w) ≤ aj(w) for all 0 ≤ i < j ≤ `(w) − i. Their proof uses the hard Lefschetz property in intersection cohomology. In this note we extend Björner and Ekedahl’s theorem to all Coxeter groups using the hard Lefschetz ...