… metrics on the same manifold decreases the volume, whenever … Certain arguments of the
proof of the volume growth theorem are … of non-flat Finsler tori without conjugate points do exist. …

… of asymptotic invariants of Riemannian tori (eg see [BuI] and references there). By asymptotic
… In [BuI] we show that the asymptotic volume growth of a Riemannian torus is at least as fast …

… We consider bond percolation on these tori with edge occupation probability p and write
PT,p and ET,p for the product measure and corresponding expectation, respectively. We use …

… there), and the proof heavily relies on asymptotic geometry of tori. We believe that it is more
… on, we will be concerned with symplectic volume. We reserve the notation Vol for this volume…

… tori for a family of maps of the form (1). Although this algorithm can be applied to arbitrary
volume-preserving maps with codimension-one tori, … The method is based on a Fourier series …

… We study asymptotics of the dimer model on large toric graphs. Let \({\mathbb {L}}\) be a
weighted \(\mathbb {Z}^2\)-periodic planar graph, and let \(\mathbb {Z}^2 E\) be a large-index …

… on arithmetic and birational properties of algebraic tori which culminated in his monograph
“Algebraic Tori” … [BT95], [BT98]: the constant appearing in the asymptotic formula of Peyre [Pe] …

… the simplicial volume. In particular, we extend our computations to mapping tori of certain …
2 we collect some simple observations on mapping tori. In Sect. 3 we prove Theorem 1.7. …

… asymptotic formula provides a link between the complexity of these graphs and the height of
associated real tori, and allows us to deduce some corollaries on … of flat tori of volume 1, h ( …

… In this paper, we focus on rotationally symmetric immersed tori. Conjecturally, the … tori
that are only immersed [9]. If we have a mean curvature flow with a singularity modeled on a …