In this article we provide a vertical height estimate for compact special Weingarten surfaces of elliptic type in M2(c) × R, i.e. surfaces whose mean curvature H and extrinsic Gauss curvature Ke satisfy H = f(H2 −Ke) with 4x(f ′(x))2 < 1, for all x ∈ [0,+∞). The vertical height estimate generalizes a result by Rosenberg and Sa Earp and applies only to surfaces verifying a height estimate condit...

Let A be a subset of F p , the field of p elements with p prime. We let A + A = {a + b : a ∈ A, b ∈ A}, and AA = {ab : a ∈ A, b ∈ A}. It is fun (and useful) to prove lower bounds on max(|A+A|, |AA|) (see e.g. [BKT],[BGK],[G]). Recently, Garaev [G] showed that when |A| < p 1 2 one has the estimate max(|A + A|, |AA|) |A| 15 14. By using Plunneke's inequality in a slightly more sophisticated way, ...

This article gives estimates on the covering numbers and diameters of random proportional sections and projections of quasi-convex bodies in R. These results were known for the convex case and played an essential role in the development of the theory. Because duality relations cannot be applied in the quasi-convex setting, new ingredients were introduced that give new understanding for the conv...

In this paper, direct estimate of Sobolev exponent of reenable distributions and its application to the asymptotic estimate of Sobolev exponent of M band Daubechies' scaling functions are considered.

Let K be an n-dimensional convex body. Define the difference body by K − K = {x − y | x, y ∈ K}. We estimate the volume of the section of K − K by a linear subspace F via the maximal volume of sections of K parallel to F. We prove that for any m-dimensional subspace F there exists x ∈ R n , such that vol ((K − K) ∩ F) ≤ C m min n m , √ m m · vol (K ∩ (F + x)) , for some absolute constant C. We ...

Distance to the Whirlpool Galaxy (M51, NGC 5194) is estimated using published pho-tometry and spectroscopy of the Type II-P supernova SN 2005cs. Both the Expanding Photosphere Method (EPM) and the Standard Candle Method (SCM), suitable for SNe II-P, were applied. The average distance (7.1 ± 1.2 Mpc) is in good agreement with earlier SBF-and PNLF-based distances, but slightly longer than the dis...

Let B 2 denote the Euclidean ball in IR , and, given closed star-shaped body K ⊂ IR, MK denote the average of the gauge of K on the Euclidean sphere. Let p ∈ (0, 1) and let K ⊂ IR be a p-convex body. In [17] we proved that for every λ ∈ (0, 1) there exists an orthogonal projection P of rank (1− λ)n such that f(λ) MK PB 2 ⊂ PK, where f(λ) = cpλ for some positive constant cp depending on p only. ...

In this note, we obtain a sharp volume estimate for complete gradient Ricci solitons with scalar curvature bounded below by a positive constant. Using Chen-Yokota’s argument we obtain a local lower bound estimate of the scalar curvature for the Ricci flow on complete manifolds. Consequently, one has a sharp estimate of the scalar curvature for expanding Ricci solitons; we also provide a direct ...

In this paper we develop a theory of matrix completion for the extreme case of noisy 1-bit observations. Instead of observing a subset of the real-valued entries of a matrix M , we obtain a small number of binary (1-bit) measurements generated according to a probability distribution determined by the realvalued entries of M . The central question we ask is whether or not it is possible to obtai...