发表与经典分析、偏微分方程、代数几何、微分几何和拓扑相关的高质量论文。

The journal "Communications in Analysis and Geometry" publishes high-quality research papers related to classical analysis, partial differential equations, algebraic geometry, differential geometry, and topology.

《Communications in Analysis and Geometry》期刊发表与经典分析、偏微分方程、代数几何、微分几何和拓扑相关的高质量研究论文。

Communications in Analysis and Geometry

We prove several new restrictions on the Euler characteristic and signature of oriented 4-manifolds with (positively or negatively) pinched sectional curvature. In particular, we show that simply connected 4-manifolds with $\delta\leq \sec\leq 1$, where $\delta=\frac{1}{1+3\sqrt3}\cong 0.161$, are homeomorphic to $S^4$ or $\mathbb C P^2$.

Renato G. Bettiol

Mario Kummer

Ricardo A. E. Mendes

Geography of pinched four-manifolds

受挤压的四维流形的几何

We investigate the prescribed Ricci curvature problem in the class of left-invariant naturally reductive Riemannian metrics on a non-compact simple Lie group. We obtain a number of conditions for the solvability of the underlying equations and discuss several examples.

Romina M. Arroyo

Mark D. Gould

Artem Pulemotov

The prescribed Ricci curvature problem for naturally reductive metrics on non-compact simple Lie groups

非紧单李群上自然约化度量的给定Ricci曲率问题

Let $M = \mathbb R^m \sharp \mathcal R^n$ be a non-doubling manifold with two ends $\mathbb R^m \sharp \mathcal R^n$, $m > n \ge 3$. Let $\Delta$ be the Laplace--Beltrami operator which is non-negative self-adjoint on $L^2(M)$. Then $\Delta$ and its square root $\sqrt{\Delta}$ generate the semigroups $e^{-t\Delta}$ and $e^{-t\sqrt{\Delta}}$ on $L^2(M)$, respectively. We give testing conditions for the two weight inequality for the Poisson semigroup $e^{-t\sqrt{\Delta}}$ to hold in this setting. In particular, we prove that for a measure $\mu$ on $M_{+}:=M\times (0,\infty)$ and $\sigma$ on $M$: $$ \|\mathsf{P}_\sigma(f)\|_{L^2(M_{+};\mu)} \lesssim \|f\|_{L^2(M;\sigma)}, $$ with $\mathsf{P}_\sigma(f)(x,t):= \int_M \mathsf{P}_t(x,y)f(y) \,d\sigma(y)$ if and only if testing conditions hold for the Poisson semigroup and its adjoint. Further, the norm of the operator is shown to be equivalent to the best constant in these testing conditions.

Xuan Thinh Duong

Ming-Yi Lee

Ji Li

Brett D. Wick

The two weight inequality for the Poisson semigroup on manifold with ends

带有端流形上泊松半群的双权不等式

In this article, we extend Huisken's theorem that convex surfaces flow to round points by mean curvature flow. We construct certain classes of mean convex and non-mean convex hypersurfaces that shrink to round points and use these constructions to create pathological examples of flows. We find a sequence of flows that exist on a uniform time interval, have uniformly bounded diameter, and shrink to round points, yet the sequence of initial surfaces has no subsequence converging in the Gromov-Hausdorff sense. Moreover, we find a sequence of flows which all shrink to round points, yet the initial surfaces converge to a space-filling surface. Also constructed are surfaces of arbitrarily large area which are close in Hausdorff distance to the round sphere yet shrink to round points.

Alexander Mramor

Alec Payne

Nonconvex surfaces which flow to round points

非凸曲面流向圆点

We show that if $M$ is any closed, orientable hyperbolic $3$-manifold with ${\rm vol} M\le3.69$, we have ${\rm dim} H_1(M;{\bf F}_2)\le7$. This may be regarded as a qualitative improvement of a result due to Culler and Shalen, because the constant $3.69$ is greater than the ordinal corresponding to $\omega^2$ in the well-ordered set of finite volumes of hyperbolic $3$-manifolds. We also show that if ${\rm vol} M\le 3.77$, we have ${\rm dim} H_1(M;{\bf F}_2)\le10$. 
These results are applications of a new method for obtaining lower bounds for the volume of a closed, orientable hyperbolic $3$-manifold such that $\pi_1(M)$ is $k$-free for a given $k\ge4$. Among other applications we show that if $\pi_1(M)$ is $4$-free we have ${\rm vol} M>3.57$ (improving the lower bound of $3.44$ given by Culler and Shalen), and that if $\pi_1(M)$ is $5$-free we have ${\rm vol} M>3.77$.

短名
Journal Impact	0.65
国际分区	MATHEMATICS(Q2)
期刊索引	SCI Q3中科院 4 区

ISSN	1019-8385, 1944-9992
h-index	47
国内分区	数学(4区)数学数学(4区)

涉及主题	数学纯数学数学分析几何学物理量子力学组合数学工程类曲率计算机科学数学物理标量曲率
出版信息	出版商: International Press of Boston, Inc.，出版周期: Bimonthly，期刊类型: journal，开源期刊: 否
基本数据	创刊年份: 1996，原创研究文献占比: 100.00%，自引率:0.00%， Gold OA占比: 0.00%
平均审稿周期	网友分享经验：>12周，或约稿
平均录用比例	网友分享经验：容易

Communications in Analysis and Geometry

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Geography of pinched four-manifolds

The prescribed Ricci curvature problem for naturally reductive metrics on non-compact simple Lie groups

The two weight inequality for the Poisson semigroup on manifold with ends

Nonconvex surfaces which flow to round points

Hyperbolic volume, mod 2 homology, and $k$-freeness

Geography of pinched four-manifolds

The prescribed Ricci curvature problem for naturally reductive metrics on non-compact simple Lie groups

The two weight inequality for the Poisson semigroup on manifold with ends

Nonconvex surfaces which flow to round points

Hyperbolic volume, mod 2 homology, and $k$-freeness