10,939 research outputs found
On the volume functional of compact manifolds with boundary with constant scalar curvature
We study the volume functional on the space of constant scalar curvature
metrics with a prescribed boundary metric. We derive a sufficient and necessary
condition for a metric to be a critical point, and show that the only domains
in space forms, on which the standard metrics are critical points, are geodesic
balls. In the zero scalar curvature case, assuming the boundary can be
isometrically embedded in the Euclidean space as a compact strictly convex
hypersurface, we show that the volume of a critical point is always no less
than the Euclidean volume bounded by the isometric embedding of the boundary,
and the two volumes are equal if and only if the critical point is isometric to
a standard Euclidean ball. We also derive a second variation formula and apply
it to show that, on Euclidean balls and ''small'' hyperbolic and spherical
balls in dimensions 3 to 5, the standard space form metrics are indeed saddle
points for the volume functional
Journal Staff
Discoba (Excavata) is an ancient group of eukaryotes with great morphological and ecological diversity. Unlike the other major divisions of Discoba (Jakobida and Euglenozoa), little is known about the mitochondrial DNAs(mtDNAs) of Heterolobosea. We have assembled a complete mtDNA genome from the aggregating heterolobosean amoeba, Acrasis kona, which consists of a single circular highly AT-rich (83.3%) molecule of 51.5 kb. Unexpectedly, A. kona mtDNA is missing roughly 40% of the protein-coding genes and nearly half of the transfer RNAs found in the only other sequenced heterolobosean mtDNAs, those of Naegleria spp. Instead, over a quarter of A. kona mtDNA consists of novel open reading frames. Eleven of the 16 protein-coding genes missing from A. kona mtDNA were identified in its nuclear DNA and polyA RNA, and phylogenetic analyses indicate that at least 10 of these 11 putative nuclear-encoded mitochondrial (NcMt) proteins arose by direct transfer from the mitochondrion. Acrasis kona mtDNA also employs C-to-U type RNA editing, and 12 homologs of DYW-type pentatricopeptide repeat (PPR) proteins implicated in plant organellar RNA editing are found in A. kona nuclear DNA. A mapping of mitochondrial gene content onto a consensus phylogeny reveals a sporadic pattern of relative stasis and rampant gene loss in Discoba. Rampant loss occurred independently in the unique common lineage leading to Heterolobosea + Tsukubamonadida and later in the unique lineage leading to Acrasis. Meanwhile, mtDNA gene content appears to be remarkably stable in the Acrasis sister lineage leading to Naegleria and in their distant relatives Jakobida
On a Localized Riemannian Penrose Inequality
Consider a compact, orientable, three dimensional Riemannian manifold with
boundary with nonnegative scalar curvature. Suppose its boundary is the
disjoint union of two pieces: the horizon boundary and the outer boundary,
where the horizon boundary consists of the unique closed minimal surfaces in
the manifold and the outer boundary is metrically a round sphere. We obtain an
inequality relating the area of the horizon boundary to the area and the total
mean curvature of the outer boundary. Such a manifold may be thought as a
region, surrounding the outermost apparent horizons of black holes, in a
time-symmetric slice of a space-time in the context of general relativity. The
inequality we establish has close ties with the Riemannian Penrose Inequality,
proved by Huisken and Ilmanen, and by Bray.Comment: 16 page
Dirichlet Boundary State in Linear Dilaton Background
Dirichlet-branes have emerged as important objects in studying
nonperturbative string theory. It is important to generalize these objects to
more general backgrounds other than the usual flat background. The simplest
case is the linear dilaton condensate. The usual Dirichlet boundary condition
violates conformal invariance in such a background. We show that by switching
on a certain boundary interaction, conformal invariance is restored. An
immediate application of this result is to two dimensional string theory.Comment: 6 pages, harvmac, some remarks are modified and one reference is
added, formulas remain the sam
Descriptions of membrane mechanics from microscopic and effective two-dimensional perspectives
Mechanics of fluid membranes may be described in terms of the concepts of
mechanical deformations and stresses, or in terms of mechanical free-energy
functions. In this paper, each of the two descriptions is developed by viewing
a membrane from two perspectives: a microscopic perspective, in which the
membrane appears as a thin layer of finite thickness and with highly
inhomogeneous material and force distributions in its transverse direction, and
an effective, two-dimensional perspective, in which the membrane is treated as
an infinitely thin surface, with effective material and mechanical properties.
A connection between these two perspectives is then established. Moreover, the
functional dependence of the variation in the mechanical free energy of the
membrane on its mechanical deformations is first studied in the microscopic
perspective. The result is then used to examine to what extent different,
effective mechanical stresses and forces can be derived from a given, effective
functional of the mechanical free energy.Comment: 37 pages, 3 figures, minor change
New remarks on the linear constraint self-dual boson and Wess-Zumino terms
In this work we prove in a precise way that the soldering formalism can be
applied to the Srivastava chiral boson (SCB), in contradiction with some
results appearing in the literature. We have promoted a canonical
transformation that shows directly that the SCB is composed of two
Floreanini-Jackiw's particles with the same chirality which spectrum is a
vacuum-like one. As another conflictive result we have proved that a
Wess-Zumino term used in the literature consists of the scalar field, once
again denying the assertion that the WZ term adds a new degree of freedom to
the SCB theory in order to modify the physics of the system.Comment: 6 pages, Revtex. Final version to appear in Physical Review
Low regularity solutions of two fifth-order KdV type equations
The Kawahara and modified Kawahara equations are fifth-order KdV type
equations and have been derived to model many physical phenomena such as
gravity-capillary waves and magneto-sound propagation in plasmas. This paper
establishes the local well-posedness of the initial-value problem for Kawahara
equation in with and the local well-posedness
for the modified Kawahara equation in with .
To prove these results, we derive a fundamental estimate on dyadic blocks for
the Kawahara equation through the multiplier norm method of Tao
\cite{Tao2001} and use this to obtain new bilinear and trilinear estimates in
suitable Bourgain spaces.Comment: 17page
Vesicles in solutions of hard rods
The surface free energy of ideal hard rods near curved hard surfaces is
determined to second order in curvature for surfaces of general shape. In
accordance with previous results for spherical and cylindrical surfaces it is
found that this quantity is non-analytical when one of the principal curvatures
changes signs. This prohibits writing it in the common Helfrich form. It is
shown that the non-analytical terms are the same for any aspect ratio of the
rods. These results are used to find the equilibrium shape of vesicles immersed
in solutions of rod-like (colloidal) particles. The presence of the particles
induces a change in the equilibrium shape and to a shift of the prolate-oblate
transition in the vesicle phase diagram, which are calculated within the
framework of the spontaneous curvature model. As a consequence of the special
form of the energy contribution due to the rods these changes cannot be
accounted for by a simple rescaling of the elastic constants of the vesicle as
for solutions of spherical colloids or polymers.Comment: 11 pages, 7 figures, submitted to Phys. Rev.
The mutation Ser2117Leu, in the second hydrophobic spike of the factor V C2 domain, increases phospholipid affinity and specific activity
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/106082/1/jth05227.pd
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