Thesis (Doctoral)--Universität Bonn, 1990. / Includes bibliographical references.

Thesis (Doctoral)--Ruhr-Universität Bochum, [1991] / Includes bibliographical references.

Thesis (PH. D.)--Cornell University. / Reprinted from the American Journal of Mathematics, vol. XXIX, no. 4.

Thesis (Ph. D.)--Lehigh University, 2006. / Includes vita. Includes bibliographical references (leaves 72-76).

Abstract Not Provided. / Thesis / Master of Science (MSc)

Indispensable to all modes of migration used during single cell metastasis, cytoplasmic protrusions are pivotal in surveying cells local surroundings which ultimately initiates migration of the cell body. Cancer cell migration is fairly well studied with the traditional focus on protrusion driven cell body displacement, while less is known on the role of protrusions in sensing cellular microenvironments. Here, we present a suspended and aligned fiber platform capable of high spatio-temporal imaging of protrusions capable of sensing fiber curvature contrasts independent of cell migration. By varying the diameter of suspended fibers, we are able to maintain cell migration along low curvature-large diameter (2μm) fibers, while solely allowing cells to sense, initiate, and mature protrusions on orthogonally deposited high curvature-low diameter (~100, 200 and 600 nm) fibers. Using highly aggressive breast MDA-MB-231 and brain glioblastoma DBTRG-05MG model systems, we find that MDA-MB-231 protrusion maturation dynamics are more sensitive to changes in fiber curvature and fibronectin ligand coating concentration compared to DBTRG-05MG. Furthermore, we find that vimentin intermediate filaments localize within 70% of mature protrusions, which normally form on larger diameter fibers. Additionally, protrusion lengths fluctuate continuously until the protrusion is either terminated or stabilized, and occasionally protrusions are observed to shed cytoplasmic fragments. Through manipulation of curvature contrasts, we demonstrate single protrusive hierarchical decomposition and coordination in zeroth (main), first and second order branches. The fiber curvature platform presented here uniquely allows cancer cells to sense nanofiber curvature contrasts, thus providing new mechanistic insights in protrusion initiation, maturation, and hierarchical coordination. / Master of Science

Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / O objetivo desta dissertaÃÃo à apresentar uma demonstraÃÃo para uma desigualdade pontual, denominada conjectura da curvatura escalar normal, a qual à vÃlida para subvariedades n-dimensionais, Mn, imersas isometricamente em formas espaciais Nn+m(c) de curvatura seccional constante c. / In this work we present a proof of the Normal Scalar Curvature Conjecture for submanifolds Mn, isometrically immersed into space forms Nn+m(c) of constant sectional curvature c.

This thesis consists of two parts. In the first part, we study certain Ricci flow invariant nonnegative curvature conditions as given by B. Wilking. We begin by proving that any such nonnegative curvature implies nonnegative isotropic curvature in the Riemannian case and nonnegative orthogonal bisectional curvature in the K¨ahler case. For any closed AdSO(n,C) invariant subset S so(n, C) we consider the notion of positive curvature on S, which we call positive S- curvature. We show that the class of all such subsets can be naturally divided into two subclasses: The first subclass consists of those sets S for which the following holds: If two Riemannian manifolds have positive S- curvature then their connected sum also admits a Riemannian metric of positive S- curvature. The other subclass consists of those sets for which the normalized Ricci flow on a closed Riemannian manifold with positive S-curvature converges to a metric of constant positive sectional curvature. In the second part of the thesis, we study the behavior of Ricci flow for a manifold having positive S - curvature, where S is in the first subclass. More specifically, we study the Ricci flow for a special class of metrics on Sp+1 x S1 , p ≥ 4, which have positive isotropic curvature.

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No description available.