Teichmüller theory and collapse of flat manifolds

We provide an algebraic description of the Teichmüller space and moduli space of flat metrics on a closed manifold or orbifold and study its boundary, which consists of (isometry classes of) flat orbifolds to which the original object may collapse. It is also shown that every closed flat orbifold can be obtained by collapsing closed flat manifolds, and the collapsed limits of closed flat 3-manifolds are classified

Sectional curvature and Weitzenb\"ock formulae

We establish a new algebraic characterization of sectional curvature bounds $\sec\geq k$ and $\sec\leq k$ using only curvature terms in the Weitzenb\"ock formulae for symmetric $p$-tensors. By introducing a symmetric analogue of the Kulkarni-Nomizu product, we provide a simple formula for such curvature terms. We also give an application of the Bochner technique to closed $4$-manifolds with indefinite intersection form and $\sec>0$ or $\sec\geq0$, obtaining new insights into the Hopf Conjecture, without any symmetry assumptions.Comment: LaTeX2e, 25 pages, final version. To appear in Indiana Univ. Math.

Strongly positive curvature

We begin a systematic study of a curvature condition (strongly positive curvature) which lies strictly between positive curvature operator and positive sectional curvature, and stems from the work of Thorpe in the 1970s. We prove that this condition is preserved under Riemannian submersions and Cheeger deformations, and that most compact homogeneous spaces with positive sectional curvature satisfy it.Comment: LaTeX2e, 26 page

Controlling metamaterial resonances via dielectric and aspect ratio effects

We study ways to enhance the sensitivity and dynamic tuning range of the fundamental inductor-capacitor (LC) resonance in split ring resonators (SRRs) by controlling the aspect ratio of the SRRs and their substrate thickness. We conclude that both factors can significantly affect the LC resonance. We show that metafilms consisting of low height SRRs on a thin substrate are most sensitive to changes in their dielectric environment and thus show excellent potential for sensing applications.Comment: 4 pages with 4 figure

Radiação, especialmente a UV-B, como fator limitante à germinação de urediósporos de Hemileia vastatrix.

Objetivou-se avaliar a capacidade germinativa de urediniósporos de Hemileia vastatrix submetidos a diferentes doses de radiação UV-B. Urediniósporos de H. vastatrix coletados de lesões jovens da ferrugem do cafeeiro foram suspendidos em água contendo Tween 80 (0,02%), alíquotas de 20?L foram transferidas para placas de Petri contendo ágar-água. Os urediniósporos foram imediatamente expostos a seis diferentes doses de radiação UV-B e incubados durante 12 e 24 h. Avaliou-se um total de 300 urediniósporos/repetição considerando como germinado todos aqueles que apresentavam tubo germinativo formado com comprimento igual ou superior ao seu maior diâmetro. A inibição da germinação dos urediniósporos de H. vastatrix, mesmo decorridos 24h de sua germinação, foi diretamente proporcional ao aumento nos níveis de radiação UV-B. O decréscimo na germinação foi proporcional ao aumento das doses de UV-B, indicando que o aumento nos níveis de radiação UV-B pode constituir em um fator limitante para o desenvolvimento da infecção da ferrugem do cafeeiro