Special K\"ahler-Ricci potentials on compact K\"ahler manifolds

A special K\"ahler-Ricci potential on a K\"ahler manifold is any nonconstant $C^\infty$ function $\tau$ such that $J(\nabla\tau)$ is a Killing vector field and, at every point with $d\tau\ne 0$, all nonzero tangent vectors orthogonal to $\nabla\tau$ and $J(\nabla\tau)$ are eigenvectors of both $\nabla d\tau$ and the Ricci tensor. For instance, this is always the case if $\tau$ is a nonconstant $C^\infty$ function on a K\"ahler manifold $(M,g)$ of complex dimension $m>2$ and the metric $\tilde g=g/\tau^2$, defined wherever $\tau\ne 0$, is Einstein. (When such $\tau$ exists, $(M,g)$ may be called {\it almost-everywhere conformally Einstein}.) We provide a complete classification of compact K\"ahler manifolds with special K\"ahler-Ricci potentials and use it to prove a structure theorem for compact K\"ahler manifolds of any complex dimension $m>2$ which are almost-everywhere conformally Einstein.Comment: 45 pages, AMSTeX, submitted to Journal f\"ur die reine und angewandte Mathemati

New DRIE-Patterned Electrets for Vibration Energy Harvesting

This paper is about a new manufacturing process aimed at developing stable SiO2/Si3N4 patterned electrets using a Deep Reactive Ion Etching (DRIE) step for an application in electret-based Vibration Energy Harvesters (e-VEH). This process consists in forming continuous layers of SiO2/Si3N4 electrets in order to limit surface conduction phenomena and is a new way to see the problem of electret patterning. Experimental results prove that patterned electrets charged by a positive corona discharge show excellent stability with high surface charge densities that may reach 5mC/m^2 on 1.1\mu m-thick layers, even with fine patterning and harsh temperature conditions (up to 250{\deg}C). This paves the way to new e-VEH designs and manufacturing processes.Comment: Proc. European Energy Conference, 201

Autoimmunity

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66083/1/j.1365-4362.1981.tb00393.x.pd

Hamiltonian 2-forms in Kahler geometry, III Extremal metrics and stability

This paper concerns the explicit construction of extremal Kaehler metrics on total spaces of projective bundles, which have been studied in many places. We present a unified approach, motivated by the theory of hamiltonian 2-forms (as introduced and studied in previous papers in the series) but this paper is largely independent of that theory. We obtain a characterization, on a large family of projective bundles, of those `admissible' Kaehler classes (i.e., the ones compatible with the bundle structure in a way we make precise) which contain an extremal Kaehler metric. In many cases, such as on geometrically ruled surfaces, every Kaehler class is admissible. In particular, our results complete the classification of extremal Kaehler metrics on geometrically ruled surfaces, answering several long-standing questions. We also find that our characterization agrees with a notion of K-stability for admissible Kaehler classes. Our examples and nonexistence results therefore provide a fertile testing ground for the rapidly developing theory of stability for projective varieties, and we discuss some of the ramifications. In particular we obtain examples of projective varieties which are destabilized by a non-algebraic degeneration.Comment: 40 pages, sequel to math.DG/0401320 and math.DG/0202280, but largely self-contained; partially replaces and extends math.DG/050151

Bounding λ2 for Kähler–Einstein metrics with large symmetry groups

We calculate an upper bound for the second non-zero eigenvalue of the scalar Laplacian, λ2, for toric-Kähler–Einstein metrics in terms of the polytope data. We also give a similar upper bound for Koiso–Sakane type Kähler–Einstein metrics. We provide some detailed examples in complex dimensions 1, 2 and 3

The HIV-1 Tat Protein is Monomethylated at Lysine 71 by the Lysine Methyltransferase KMT7

The HIV-1 transactivator protein Tat is a critical regulator of HIV transcription primarily enabling efficient elongation of viral transcripts. Its interactions with RNA and various host factors are regulated by ordered, transient post-translational modifications. Here, we report a novel Tat modification, monomethylation at lysine 71 (K71). We found that Lys-71 monomethylation (K71me) is catalyzed by KMT7, a methyltransferase that also targets lysine 51 (K51) in Tat. Using mass spectrometry, in vitro enzymology, and modification-specific antibodies, we found that KMT7 monomethylates both Lys-71 and Lys-51 in Tat. K71me is important for full Tat transactivation, as KMT7 knockdown impaired the transcriptional activity of wild type (WT) Tat but not a Tat K71R mutant. These findings underscore the role of KMT7 as an important monomethyltransferase regulating HIV transcription through Tat

An extremal eigenvalue problem in Kähler geometry

We study Laplace eigenvalues λk on Kähler manifolds as functionals on the space of Kähler metrics with cohomologous Kähler forms. We introduce a natural notion of a λk-extremal Kähler metric and obtain necessary and sufficient conditions for it. A particular attention is paid to the λ1-extremal properties of Kähler–Einstein metrics of positive scalar curvature on manifolds with non-trivial holomorphic vector fields