4,017 research outputs found
Non-rigidity of spherical inversive distance circle packings
We give a counterexample of Bowers-Stephenson's conjecture in the spherical
case: spherical inversive distance circle packings are not determined by their
inversive distances.Comment: 6 pages, one pictur
Minimal surfaces and particles in 3-manifolds
We use minimal (or CMC) surfaces to describe 3-dimensional hyperbolic,
anti-de Sitter, de Sitter or Minkowski manifolds. We consider whether these
manifolds admit ``nice'' foliations and explicit metrics, and whether the space
of these metrics has a simple description in terms of Teichm\"uller theory. In
the hyperbolic settings both questions have positive answers for a certain
subset of the quasi-Fuchsian manifolds: those containing a closed surface with
principal curvatures at most 1. We show that this subset is parameterized by an
open domain of the cotangent bundle of Teichm\"uller space. These results are
extended to ``quasi-Fuchsian'' manifolds with conical singularities along
infinite lines, known in the physics literature as ``massive, spin-less
particles''.
Things work better for globally hyperbolic anti-de Sitter manifolds: the
parameterization by the cotangent of Teichm\"uller space works for all
manifolds. There is another description of this moduli space as the product two
copies of Teichm\"uller space due to Mess. Using the maximal surface
description, we propose a new parameterization by two copies of Teichm\"uller
space, alternative to that of Mess, and extend all the results to manifolds
with conical singularities along time-like lines. Similar results are obtained
for de Sitter or Minkowski manifolds.
Finally, for all four settings, we show that the symplectic form on the
moduli space of 3-manifolds that comes from parameterization by the cotangent
bundle of Teichm\"uller space is the same as the 3-dimensional gravity one.Comment: 53 pages, no figure. v2: typos corrected and refs adde
The induced metric on the boundary of the convex hull of a quasicircle in hyperbolic and anti-de Sitter geometry
Celebrated work of Alexandrov and Pogorelov determines exactly which metrics on the sphere are induced on the boundary of a compact convex subset of hyperbolic three-space. As a step toward a generalization for unbounded convex subsets, we consider convex regions of hyperbolic three-space bounded by two properly embedded disks which meet at infinity along a Jordan curve in the ideal boundary. In this setting, it is natural to augment the notion of induced metric on the boundary of the convex set to include a gluing map at infinity which records how the asymptotic geometry of the two surfaces compares near points of the limiting Jordan curve. Restricting further to the case in which the induced metrics on the two bounding surfaces have constant curvature K 2 Œ 1; 0/ and the Jordan curve at infinity is a quasicircle, the gluing map is naturally a quasisymmetric homeomorphism of the circle. The main result is that for each value of K, every quasisymmetric map is achieved as the gluing map at infinity along some quasicircle. We also prove analogous results in the setting of three-dimensional anti-de Sitter geometry. Our results may be viewed as universal versions of the conjectures of Thurston and Mess about prescribing the induced metric on the boundary of the convex core of quasifuchsian hyperbolic manifolds and globally hyperbolic anti-de Sitter spacetimes
Quasicircles and width of Jordan curves in CP1
We study a notion of ‘width’ for Jordan curves in (Formula presented.), paying special attention to the class of quasicircles. The width of a Jordan curve is defined in terms of the geometry of its convex hull in hyperbolic three-space. A similar invariant in the setting of anti-de Sitter geometry was used by Bonsante–Schlenker to characterize quasicircles among a larger class of Jordan curves in the boundary of anti de Sitter space. In contrast to the AdS setting, we show that there are Jordan curves of bounded width which fail to be quasicircles. However, we show that Jordan curves with small width are quasicircles
Non-Fermi liquid angle resolved photoemission lineshapes of Li0.9Mo6O17
A recent letter by Xue et al. (PRL v.83, 1235 ('99)) reports a Fermi-Liquid
(FL) angle resolved photoemission (ARPES) lineshape for quasi one-dimensional
Li0.9Mo6O17, contradicting our report (PRL v.82, 2540 ('99)) of a non-FL
lineshape in this material. Xue et al. attributed the difference to the
improved angle resolution. In this comment, we point out that this reasoning is
flawed. Rather, we find that their data have fundamental differences from other
ARPES results and also band theory.Comment: To be published as a PRL Commen
Collisions of particles in locally AdS spacetimes I. Local description and global examples
We investigate 3-dimensional globally hyperbolic AdS manifolds containing
"particles", i.e., cone singularities along a graph . We impose
physically relevant conditions on the cone singularities, e.g. positivity of
mass (angle less than on time-like singular segments). We construct
examples of such manifolds, describe the cone singularities that can arise and
the way they can interact (the local geometry near the vertices of ).
We then adapt to this setting some notions like global hyperbolicity which are
natural for Lorentz manifolds, and construct some examples of globally
hyperbolic AdS manifolds with interacting particles.Comment: This is a rewritten version of the first part of arxiv:0905.1823.
That preprint was too long and contained two types of results, so we sliced
it in two. This is the first part. Some sections have been completely
rewritten so as to be more readable, at the cost of slightly less general
statements. Others parts have been notably improved to increase readabilit
On the total mean curvature of non-rigid surfaces
Using Green's theorem we reduce the variation of the total mean curvature of
a smooth surface in the Euclidean 3-space to a line integral of a special
vector field and obtain the following well-known theorem as an immediate
consequence: the total mean curvature of a closed smooth surface in the
Euclidean 3-space is stationary under an infinitesimal flex.Comment: 4 page
Non-fermi-liquid single particle lineshape of the quasi-one-dimensional non-CDW metal Li_{0.9}Mo_{6}O_{17} : comparison to the Luttinger liquid
We report the detailed non-Fermi liquid (NFL) lineshape of the dispersing
excitation which defines the Fermi surface (FS) for quasi-one-dimensional
Li_{0.9}Mo_{6}O_{17}. The properties of Li_{0.9}Mo_{6}O_{17} strongly suggest
that the NFL behavior has a purely electronic origin. Relative to the
theoretical Luttinger liquid lineshape, we identify significant similarities,
but also important differences.Comment: 5 pages, 3 eps figure
Polyethylene glycol-coated collagen patch (hemopatch®) in open partial nephrectomy
PURPOSE To describe the results of a polyethylene glycol-coated collagen patch, Hemopatch® on blood loss, surgical time and renal function in partial nephrectomy (PN) for renal cell carcinoma (RCC). METHODS Out of a single surgeon cohort of n = 565 patients undergoing conventional open PN (CPN) between 01/2015 and 12/2017 at the University of Munich a consecutive subgroup (n = 42) was operated on using a polyethylene glycol-coated collagen-based sealant Hemopatch® (Baxter International Inc., Deerfield, IL, USA) (HPN). RESULTS Median age was 65.2~years (range 12.7-95.2) with median follow-up of 9.43~months (0.03-49.15). Baseline renal function (CKD-EPI) was 78.56~ml/min/1.73~m2 (range 20.38-143.09) with a non-significant decline to 74.78~ml/min/1.73~m2 (range 3.75-167.74) at follow-up. In CPN 46% had low complexity, 33% moderate complexity and 20% high complexity lesions with 33% low, 40% moderate and 27% high complexity masses in HPN. Median tumor size was 4.3~cm (range 1-38~cm) in CPN with 4.8~cm (range 3.8-18.3~cm) with HPN, p = 0.293. Median blood loss and duration of surgery was significantly lower in the HPN group vs. CPN (146~ml ± 195 vs. 114~ml ± 159~ml; p = 0.021; 43~min ± 27 for HPN vs. 53~min ± 49; p = 0.035) with no difference in clamping time (12.6~min ± 8.6 for HPN vs. 12.0~min ± 9.5; p = 0.701). CONCLUSIONS Hemopatch® supported renoraphy shows promising results compared to standard renoraphy in PN. No side effects were seen. Further studies should evaluate the prevention of arterio-venous or urinary fistulas. In complex partial nephrectomies Hemopatch® supported renoraphy should be considered
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