We revisit the classical Poincaré inequality on closed surfaces, and prove its natural analogue for quadratic differentials. In stark contrast to the classical case, our inequality does not degenerate when we work on hyperbolic surfaces that themselves are degenerating, and this fact turns out to be essential for applications to the Teichmüller harmonic map flow.

In this paper we studied the translation surfaces according to a new frame called q-frame in three dimensional Euclidean space. The curvatures of the translation surface are obtained in terms of q-frame curvatures. Finally some special cases are investigated for these surfaces.

We prove uniqueness of instantaneously complete Ricci flows on surfaces. We do not require any bounds of any form on the curvature or its growth at infinity, nor on the metric or its growth (other than that implied by instantaneous completeness). Coupled with earlier work, particularly [25, 12], this completes the well-posedness theory for instantaneously complete Ricci flows on surfaces.

Continuing the work in [13], we show that within each stratum of translation surfaces, there is a residual set of surfaces for which the geodesic flow in almost every direction is ergodic for almost-every periodic group extension produced using a technique referred to as cuts.

In this work, we report the antimicrobial efficacy of azetidinium functionalized polytetrahydrofurans in solution and their application in the preparation of non leaching, antimicrobial surfaces. The excellent antimicrobial efficacy of these water soluble polymers both in solution and on surfaces (>99.99%–100% bacterial growth inhibition) makes them excellent candidates for solving the hygiene ...

studying gaussian beam is a method to investigate laser beam propagation and abcd matrix is a fast and simple method to simulate gaussian beam propagation in different mediums. of the abcd matrices studied so far, reflection and refraction matrices at various surfaces have attracted a lot of researches. however in previous work the incident beam and the principle axis of surface are in parallel...

The present work demonstrates a generalized strategy using water-only hydrothermal oxidation to construct complex biomimetic micronanostructures on a series of metals and alloys, resulting in superhydrophilic surfaces. This general approach is environmentally-benign and cost-effective, which offers a unique clue for the rational fabrication of micronanoscale architectures and superhydrophilic s...

In this work we obtain the group of conformal and anticonformal automorphisms of real cyclic p-gonal Riemann surfaces, where p ≥ 3 is a prime integer and the genus of the surfaces is at least (p − 1) + 1. We use Fuchsian and NEC groups, and cohomology of finite groups.

This paper describes a technique to evaluate Loop subdivision surfaces at arbitrary parameter values. The method is a straightforward extension of our evaluation work for Catmull-Clark surfaces. The same ideas are applied here, with the differences being in the details only.