Collars and partitions of hyperbolic cone-surfaces

For compact Riemann surfaces, the collar theorem and Bers' partition theorem are major tools for working with simple closed geodesics. The main goal of this paper is to prove similar theorems for hyperbolic cone-surfaces. Hyperbolic two-dimensional orbifolds are a particular case of such surfaces. We consider all cone angles to be strictly less than $\pi$ to be able to consider partitions.Comment: 11 pages, 9 figures; v2: minor changes, to appear in Geometriae Dedicat

Extraordinary Biomass-Burning Episode and Impact Winter Triggered by the Younger Dryas Cosmic Impact ∼12,800 Years Ago. 2. Lake, Marine, and Terrestrial Sediments

Part 1 of this study investigated evidence of biomass burning in global ice records, and here we continue to test the hypothesis that an impact event at the Younger Dryas boundary (YDB) caused an anomalously intense episode of biomass burning at ∼12.8 ka on a multicontinental scale (North and South America, Europe, and Asia). Quantitative analyses of charcoal and soot records from 152 lakes, marine cores, and terrestrial sequences reveal a major peak in biomass burning at the Younger Dryas (YD) onset that appears to be the highest during the latest Quaternary. For the Cretaceous-Tertiary boundary (K-Pg) impact event, concentrations of soot were previously utilized to estimate the global amount of biomass burned, and similar measurements suggest that wildfires at the YD onset rapidly consumed ∼10 million km2 of Earth’s surface, or ∼9% of Earth’s biomass, considerably more than for the K-Pg impact. Bayesian analyses and age regressions demonstrate that ages for YDB peaks in charcoal and soot across four continents are synchronous with the ages of an abundance peak in platinum in the Greenland Ice Sheet Project 2 (GISP2) ice core and of the YDB impact event (12,835–12,735 cal BP). Thus, existing evidence indicates that the YDB impact event caused an anomalously large episode of biomass burning, resulting in extensive atmospheric soot/dust loading that triggered an “impact winter.” This, in turn, triggered abrupt YD cooling and other climate changes, reinforced by climatic feedback mechanisms, including Arctic sea ice expansion, rerouting of North American continental runoff, and subsequent ocean circulation changes

Convexity of strata in diagonal pants graphs of surfaces

We prove a number of convexity results for strata of the diagonal pants graph of a surface, in analogy with the extrinsic geometric properties of strata in the Weil-Petersson completion. As a consequence, we exhibit convex flat subgraphs of every possible rank inside the diagonal pants graph

Convexity of strata in diagonal pants graphs of surfaces

We prove a number of convexity results for strata of the diagonal pants graph of a surface, in analogy with the extrinsic geometric properties of strata in the Weil-Petersson completion. As a consequence, we exhibit convex flat subgraphs of every possible rank inside the diagonal pants graph