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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Metric geometric aspects of Einstein manifolds
Einstein流形 度量几何 爱因斯坦流形 黎曼几何
2023/11/24
This lecture concerns the metric Riemannian geometry of Einstein manifolds, which is a central theme in modern differential geometry and is deeply connected to a large variety of fundamental problems ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Regularity of sub-elliptic harmonic map into non-positively curved metric space
亚椭圆谐波 非正曲线 度量空间 规律性
2022/12/8
We prove the Holder continuity of a harmonic map from a domain of a sub-Riemannian manifold into a locally compact manifold with non-positive curvature, and more generally into a non-positively curved...
三亚国际数学论坛：Curvatures of Graphs,Simplicial Complexes and Metric Spaces（Curvatures of Graphs,Simplicial Complexes and Metric Spaces ）
三亚国际数学论坛 Curvatures of Graphs Simplicial Complexes Metric Spaces
2017/1/10
Curvature is a notion originally developed in differential and Riemannian geometry. It was then discovered that curvature inequalities in Riemannian manifolds are equivalent to other geometric propert...
WEAK UNCERTAINTY PRINCIPLE FOR FRACTALS,GRAPHS AND METRIC MEASURE SPACES
Uncertainty principle p.c.f. fractal Heisenberg’s inequality measure metric spaces Poincar′ e inequality self-similar graphs Sierpinski ′ gasket uniform finitely ramified graphs
2015/12/10
We develop a new approach to formulate and prove the weak uncertainty inequality which was recently introduced by Okoudjou and Strichartz.We assume either an appropriate measure growth condition with ...
NEW EXAMPLES OF TOPOLOGICALLY EQUIVALENT S-UNIMODAL MAPS WITH DIFFERENT METRIC PROPERTIES
TOPOLOGICALLY EQUIVALENT S-UNIMODAL MAPS DIFFERENT METRIC PROPERTIES
2015/9/25
We construct examples of topologically conjugate unimodal maps, such that both of them have an absolutely continuous invariant measure, but for one of them that measure is finite, and for another one ...
Metric selection in Douglas-Rachford splitting and ADMM
Divided multiplier literature linear convergence and linear convergence parameter optimization algorithm
2015/8/7
Recently, several convergence rate results for Douglas-Rachford splitting and the alternating direction method of multipliers (ADMM) have been presented in the literature. In this paper, we show linea...
HODGE METRIC COMPLETION OF THE TEICHM¨ ULLER SPACE OF CALABI–YAU MANIFOLDS
HODGE METRIC COMPLETION TEICHM¨ ULLER SPACE CALABI–YAU MANIFOLDS
2013/5/4
We prove that the Hodge metric completion of the Teichm¨uller space of polarized and marked Calabi–Yau manifolds is a complex affine manifold. We also show that the extended period map from the comple...
On character of points in the Higson corona of a metric space
Higson corona character of a point ultrafilter number dominating number
2012/6/4
We prove that for an unbounded metric space $X$, the minimal character $m\chi(\check X)$ of a point of the Higson corona $\check X$ of $X$ is equal to $\mathfrak u$ if $X$ has asymptotically isolated ...
Optimal Riemannian metric for a volumorphism and a mean ergodic theorem in complete global Alexandrov nonpositively curved spaces
Optimal Riemannian metric volumorphism mean ergodic theorem complete global Alexandrov nonpositively curved spaces Differential Geometry
2012/6/2
In this paper we give a natural condition for when a volumorphism on a Riemannian manifold $(M,g)$ is actually an isometry with respect to some other, optimal, Riemannian metric $h$. We consider the n...
A Tale of Two Arc Lengths: Metric notions for curves in surfaces in equiaffine space
anne curve anne arc length anne surface anne first fundamental form
2012/5/1
In Euclidean geometry, all metric notions (arc length for curves, the first fundamental form for surfaces, etc.) are derived from the Euclidean inner product on tangent vectors, and this inner product...
Adapted connections on metric contact manifolds
Adapted connections metric contact manifolds Differential Geometry
2012/4/13
In this paper, we describe the space of adapted connections on a metric contact manifold through the space of their torsion tensors. The torsion tensor is an element of the space of TM-valued two-form...
Local convexity properties of Apollonian and Seittenranta's metric balls
Apollonian distance Seittenranta’s distance metric ball local convexity
2012/4/2
We consider local convexity properties of the Apollonian and the Seittenranta's metric balls. The Apollonian metric balls are considered in the twice punctured space, convex and starlike domains. The ...
On the strong metric dimension of corona product graphs and join graphs
Strong metric dimension strong resolving sets strong metric basis clique number corona graph
2012/4/2
Let $G$ be a connected graph. A vertex $w$ strongly resolves a pair $u$, $v$ of vertices of $G$ if there exists some shortest $u-w$ path containing $v$ or some shortest $v-w$ path containing $u$. A se...
Improved geodesics for the reduced curvature-dimension condition in branching metric spaces
Ricci curvature metric measure spaces branching metric spaces Differential Geometry
2012/2/29
In this note we show that in metric measure spaces satisfying the reduced curvature-dimension condition CD*(K,N) we always have geodesics in the Wasserstein space of probability measures that satisfy ...
The Metric Completion of Outer Space
The Metric Completion Outer Space the Lipschitz metric homeomorphic
2012/2/28
We prove that the completion of Outer Space with the Lipschitz metric is homeomorphic to the free splitting complex. We give a new proof of a theorem by Francaviglia and Martino [FMa] that the isometr...