ON CLOSED GEODESICS IN THE LEAF SPACE OF SINGULAR RIEMANNIAN FOLIATIONS

In this paper we prove the existence of closed geodesics in the leaf space of some classes of singular Riemannian foliations (s.r.f.), namely s.r.fs. that admit sections or have no horizontal conjugate points. We also investigate the shortening process with respect to Riemannian foliations.

An indecomposable Banach space of continuous functions which has small density

Using the method of forcing we construct a model for ZFC where CH does not hold and where there exists a connected compact topological space K of weight omega(1) < 2(omega) such that every operator on the Banach space of continuous functions on K is multiplication by a continuous function plus a weakly compact operator. In particular, the Banach space of continuous functions on K is indecomposable.

THE FUNDAMENTAL GROUP OF THE SPACE OF MAPS FROM A SURFACE INTO THE PROJECTIVE PLANE

In this work we compute the fundamental group of each connected component of the function space of maps from it closed surface into the projective space

Rigidity theorems for complete spacelike hypersurfaces with constant scalar curvature in De Sitter space

In this paper we give a partially affirmative answer to the following question posed by Haizhong Li: is a complete spacelike hypersurface in De Sitter space S(1)(n+1)(c), n >= 3, with constant normalized scalar curvature R satisfying n-2/nc <= R <= c totally umbilical? (C) 2008 Elsevier B.V. All rights reserved.

A Boolean algebra and a Banach space obtained by push-out iteration

Under the assumption that c is a regular cardinal, we prove the existence and uniqueness of a Boolean algebra B of size c defined by sharing the main structural properties that P(omega)/fin has under CH and in the N(2)-Cohen model. We prove a similar result in the category of Banach spaces. (C) 2011 Elsevier B.V. All rights reserved.

The Borsuk-Ulam theorem for homotopy spherical space forms

In this work, we show for which odd-dimensional homotopy spherical space forms the Borsuk-Ulam theorem holds. These spaces are the quotient of a homotopy odd-dimensional sphere by a free action of a finite group. Also, the types of these spaces which admit a free involution are characterized. The case of even-dimensional homotopy spherical space forms is basically known.

Bjorling problem for timelike surfaces in the Lorentz-Minkowski space

We solve the Bjorling problem for timelike surfaces in the Lorentz-Minkowski space through a split-complex representation formula obtained for this kind of surface. Our approach uses the split-complex numbers and natural split-holomorphic extensions. As applications, we show that the minimal timelike surfaces of revolution as well as minimal ruled timelike surfaces can be characterized as solutions of certain adequate Bjorling problems in the Lorentz-Minkowski space. (C) 2010 Elsevier Inc. All rights reserved.

The Gauss-Kronecker curvature of minimal hypersurfaces in four-dimensional space forms

LetQ(4)( c) be a four-dimensional space form of constant curvature c. In this paper we show that the infimum of the absolute value of the Gauss-Kronecker curvature of a complete minimal hypersurface in Q(4)(c), c <= 0, whose Ricci curvature is bounded from below, is equal to zero. Further, we study the connected minimal hypersurfaces M(3) of a space form Q(4)( c) with constant Gauss-Kronecker curvature K. For the case c <= 0, we prove, by a local argument, that if K is constant, then K must be equal to zero. We also present a classification of complete minimal hypersurfaces of Q(4)( c) with K constant.

Construction of Hamiltonian-Minimal Lagrangian submanifolds in Complex Euclidean Space

We describe several families of Lagrangian submanifolds in complex Euclidean space which are H-minimal, i.e. critical points of the volume functional restricted to Hamiltonian variations. We make use of various constructions involving planar, spherical and hyperbolic curves, as well as Legendrian submanifolds of the odd-dimensional unit sphere.

The Wijsman hyperspace of a metric hereditarily Baire space is Baire

In this paper, we show that the Wijsman hyperspace of a metric hereditarily Baire space is Baire. This solves a recent question posed by Zsilinszky. (C) 2009 Elsevier B.V. All rights reserved.

A FREE BOUNDARY ISOPERIMETRIC PROBLEM IN HYPERBOLIC 3-SPACE BETWEEN PARALLEL HOROSPHERES

We investigate the isoperimetric problem of finding the regions of prescribed volume with minimal boundary area between two parallel horospheres in hyperbolic 3-space (the part of the boundary contained in the horospheres is not included). We reduce the problem to the study of rotationally invariant regions and obtain the possible isoperimetric solutions by studying the behavior of the profile curves of the rotational surfaces with constant mean curvature in hyperbolic 3-space. We also classify all the connected compact rotational surfaces M of constant mean curvature that are contained in the region between two horospheres, have boundary partial derivative M either empty or lying on the horospheres, and meet the horospheres perpendicularly along their boundary.

Spherical space forms - Homotopy self-equivalences and homotopy types, the case of the groups Z/a x (Z/b x TL(2)(F(p)))

Let G = Z/a x(mu) (Z/b x TL(2)(F(p))) and X(n) be an n-dimensional CW-complex with the homotopy type of the n-sphere. We determine the automorphism group Aut(G) and then compute the number of distinct homotopy types of spherical space forms with respect to free and cellular G-actions on all CW-complexes X(2dn - 1), where 2d is a period of G. Next, the group E(X(2dn - 1)/alpha) of homotopy self-equivalences of spherical space forms X(2dn - 1)/alpha, associated with such G-actions alpha on X(2dn - 1) are studied. Similar results for the rest of finite periodic groups have been obtained recently and they are described in the introduction. (C) 2009 Elsevier B.V. All rights reserved.

Keratinocyte growth factor: a new mesothelial targeted therapy to reduce postoperative pericardial adhesions

Background: Several methods have been utilized to prevent pericardial and retrosternal adhesions, but none of them evaluated the mesothelial regenerative hypothesis. There are evidences that the mesothelial trauma reduces pericardial fibrinolytic capability and induces an adhesion process. Keratinocyte growth factor (KGF) has proven to improve mesothelial cells proliferation. This study investigated the influence of keratinocyte growth factor in reducing post-surgical adhesions. Methods: Twelve pigs were operated and an adhesion protocol was employed. Following a stratified randomization, the animals received a topical application of KGF or saline. At 8 weeks, intrapericardial adhesions were evaluated and a severity score was established. The time spent to dissect the adhesions and the amount of sharp dissection used, were recorded. Histological sections were stained with sirius red and morphometric analyses were assessed with a computer-assisted image analysis system. Results: The severity score was lower in the KGF group than in the control group (11.5 vs 17, p = 0.005). The dissection time was lower in the KGF group (9.2 +/- 1.4 min vs 33.9 +/- 9.2 min, p = 0.004) and presented a significant correlation with the severity score (r = 0.83, p = 0.001). A significantly less sharp dissection was also required in the KGF group. Also, adhesion area and adhesion collagen were significantly tower in the KGF group than in the control group. Conclusion: The simulation of pericardial cells with KGF reduced the intensity of postoperative adhesions and facilitated the re-operation. This study suggests that the mesothelial regeneration is the new horizon in anti-adhesion therapies. (C) 2008 European Association for Cardio-Thoracic Surgery. Published by Elsevier B.V. All rights reserved.

Synergism Between Keratinocyte Growth Factor and Carboxymethyl Chitosan Reduces Pericardial Adhesions

Background. Mesothelial injury is the pivot in the development of adhesions. An increase in the proliferation of mesothelial cells was verified by in vitro studies with the use of keratinocyte growth factor (KGF). This study investigated the influence of KGF associated with thermo-sterilized carboxymethyl chitosan (NOCCts) in the reduction of pericardial adhesions. Methods. An induction model of pericardial adhesion was carried out in 24 pigs. Animals were randomly allocated to receive topical application of KGF, KGF + NOCCts, NOCCts, or saline (control). At 8 weeks, intra-pericardial adhesions were evaluated and a severity score was established. The time spent to dissect the adhesions and the amount of sharp dissection used, were recorded. Histologic sections were stained with sirius red for a morphometric evaluation using a computer-assisted image analysis system. Cytokeratin AE1/AE3 immunostaining were employed to identify mesothelial cells. Results. The severity score expressed in median (minimum to maximum), in relation to the control group (17 [15 to 18]), was lower in the KGF + NOCCts group (7 [6 to 9], p < 0.01) followed by the KGF group (11.5 [9 to 12], 0.01 < p < 0.05) and the NOCCts group (12 [9 to 14], p > 0.05). The dissection time was significantly lower in the KGF + NOCCts group (7.1 +/- 0.6 vs 33.9 +/- 9.2 minutes, p < 0.001). A significantly less sharp dissection was also required in the KGF + NOCCts group. In the adhesion segment, a decreased collagen proportion was found in the KGF + NOCCts group (p < 0.05). Mesothelial cells were present more extensively in groups in which KGF was delivered (p = 0.01). Conclusions. The use of KGF associated with NOCCts resulted in a synergic action that decreases postoperative pericardial adhesions in a highly significant way. (Ann Thorac Surg 2010; 90: 566-72) (C) 2010 by The Society of Thoracic Surgeons

The SUMA Project: Integrating Observational Data Assessment into Space and Service Design

This presentation was offered as part of the CUNY Library Assessment Conference, Reinventing Libraries: Reinventing Assessment, held at the City University of New York in June 2014.