The rigidity of the Riemannian positive mass theorem for asymptotically hyperbolic manifolds states that the total mass of such a manifold is zero if and only if the manifold is isometric to the ...hyperbolic space. This leads to study the stability of this statement, that is, if the total mass of an asymptotically hyperbolic manifold is almost zero, is this manifold close to the hyperbolic space in any way? Motivated by the work of Huang, Lee and Sormani for asymptotically flat graphical manifolds with respect to intrinsic flat distance, we show the intrinsic flat stability of the positive mass theorem for a class of asymptotically hyperbolic graphical manifolds by adapting the positive answer to this question provided by Huang, Lee and the third named author.
We present a quasi-local version of the stability of the positive mass theorem. We work with the Brown-York quasi-local mass as it possesses positivity and rigidity properties, and therefore the ...stability of this rigidity statement can be studied. Specifically, we ask if the Brown-York mass of the boundary of some compact manifold is close to zero, must the manifold be close to a Euclidean domain in some sense? Here we consider a class of compact n-manifolds with boundary that can be realized as graphs in \mathbb{R}^{n+1}, and establish the following. If the Brown-York mass of the boundary of such a compact manifold is small, then the manifold is close to a Euclidean hyperplane with respect to the Federer-Fleming flat distance.
Let g be a metric on the 2-sphere S2 with positive Gaussian curvature and H be a positive constant. Under suitable conditions on (g, H), we construct smooth, asymptotically flat 3-manifolds M with ...non-negative scalar curvature, with outer-minimizing boundary isometric to (S2,g) and having mean curvature H, such that near infinity M is isometric to a spatial Schwarzschild manifold whose mass m can be made arbitrarily close to a constant multiple of the Hawking mass of (S2,g,H). Moreover, this constant multiplicative factor depends only on (g, H) and tends to 1 as H tends to 0. The result provides a new upper bound of the Bartnik mass associated with such boundary data.
The positive mass theorem states that the total mass of a complete asymptotically flat manifold with nonnegative scalar curvature is nonnegative; moreover, the total mass equals zero if and only if ...the manifold is isometric to the Euclidean space. Huang and Lee (Commun Math Phys 337(1):151–169,
2015
) proved the stability of the positive mass theorem for a class of
n
-dimensional (
n
≥
3
) asymptotically flat graphs with nonnegative scalar curvature, in the sense of currents. Motivated by their work and using results of Dahl et al. (Ann Henri Poincaré 14(5):1135–1168,
2013
), we adapt their ideas to obtain a similar result regarding the stability of the positive mass theorem, in the sense of currents, for a class of
n
-dimensional
(
n
≥
3
)
asymptotically hyperbolic graphs with scalar curvature bigger than or equal to
-
n
(
n
-
1
)
.
The application of air stable preformed (R)-BINAPPdBr2, (S)-BINAPPdBr2, (R)-Tol-BINAPPdBr2, and (S,S)-CHIRAPHOSPdBr2 complexes in the one-pot asymmetric reductive amination of various carbonyl ...compounds, leading to chiral amines in very good yields with high enantioselectivities (<99% ee), is reported.
In this work we provide the full description of the upper levels of the classical causal ladder for spacetimes in the context of Lorenztian length spaces, thus establishing the hierarchy between ...them. We also show that global hyperbolicity, causal simplicity, causal continuity, stable causality and strong causality are preserved under distance homothetic maps.
By works of Schoen–Yau and Gromov–Lawson any Riemannian manifold with nonnegative scalar curvature and diffeomorphic to a torus is isometric to a flat torus. Gromov conjectured subconvergence of tori ...with respect to a weak Sobolev type metric when the scalar curvature goes to 0. We prove flat and intrinsic flat subconvergence to a flat torus for noncollapsing sequences of 3-dimensional tori
M
j
that can be realized as graphs of certain functions defined over flat tori satisfying a uniform upper diameter bound and scalar curvature bounds of the form
R
g
M
j
≥
-
1
/
j
. We also show that the volume of the manifolds of the convergent subsequence converges to the volume of the limit space. We do so adapting results of Huang–Lee, Huang–Lee–Sormani and Allen–Perales–Sormani. Furthermore, our results also hold when the condition on the scalar curvature of a torus
(
M
,
g
M
)
is replaced by a bound on the quantity
-
∫
T
min
{
R
g
M
,
0
}
d
vol
g
T
, where
M
=
graph
(
f
)
,
f
:
T
→
R
and
(
T
,
g
T
)
is a flat torus. Using arguments developed by Alaee, McCormick and the first named author after this work was completed, our results hold for dimensions
n
≥
4
as well.
Antimony, a natural element that has been used as a drug for over more than 100 years, has remarkable therapeutic efficacy in patients with acute promyelocytic leukemia. This review focuses on recent ...advances in developing antimony anticancer agents with an emphasis on antimony coordination complexes, Sb （Ⅲ） and Sb （Ⅴ）. These complexes, which include many organometallic complexes, may provide a broader spectrum of antitumoral activity. They were compared with classical platinum anticancer drugs. The review covers the literature data published up to 2007. A number of antimonials with different antitumoral activities are known and have diverse applications, even though little research has been done on their possibilities. It might be feasible to develop more specific and effective inhibitors for phosphatase-targeted, anticancer therapeutics through the screening of sodium stibogluconate （SSG） and potassium antimonyltartrate-related compounds, which are comprised of antimony conjugated to different organic moieties. For example, SSG appears to be a better inhibitor than suramin which is a compound known for its antineoplastic activity against several types of cancers.
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