Ricci flow on asymptotically Euclidean manifolds YU LIIn this paper, we prove that if an manifold with nonnegative scalar curvature has long-time existence of flow, the ADM mass is nonnegative.We also give independent proof positive theorem in dimension three. 53C44; 83C99 Mass under flowWe section preserves AE condition and unchanged flow.Our argument differs from Dai Ma [16] fix coordinate system along flow.The main tool use following maximum principle noncompact evolving metrics; see [11,...

For a graph $G=(V,E)$, assigning each edge $e\in E$ weight of dual number $w(e)=1+\widehat{a}_{e}\varepsilon$, the weighted $G^{w}=(V,E,w)$ is called graph, where $-\widehat{a}_{e}$ can be regarded as perturbation unit resistor on $e$ $G$. connected $G^{w}$, we give some expressions and block representations generalized inverses Laplacian matrix $G^{w}$. And using these results, derive explicit formulas resistance distance Kirchhoff index We bounds for In particular, when only $e=\{i,j\}$...

A new boundary element method (BEM) based is described for the design of coils magnetic resonance imaging (MRI) systems. BEM an effective approach solving electromagnetic forward problem and has been used in MRI gradient coils. However, BEM-based coil faces ill-posed mathematical problem, which conventionally handled by means a Lagrange multiplication method. This work attempts to improve designs applying Tikhonov regularization scheme solve matrix system formulated model. The objective...

We give a complete classification of all $\kappa$-noncollapsed, ancient solutions to the Kahler Ricci flow with nonnegative bisectional curvature.

A generalization of moment-angle manifolds with noncontractible orbit spaces LI YUWe generalize the notion manifold over a simple convex polytope to an arbitrary nice corners.For corners Q, we first compute stable decomposition ᐆ Q via construction called rim-cubicalization Q. From this, derive formula integral cohomology group strata Q.This generalizes Hochster's for polytope.Moreover, obtain description ring using idea partial diagonal maps.In addition, define polyhedral product sequence...

In this paper we study the (equivariant) topological types of a class 3-dimensional closed manifolds (i.e., small covers), each which admits locally standard $(\mathbb{Z}_2)^3$-action such that its orbit space is simple convex 3-polytope. We introduce six equivariant operations on covers. These are interesting because their combinatorial natures. Then show cover can be obtained from $\mathbb{R}P^3$ and $S^1\times\mathbb{R}P^2$ with certain $(\mathbb{Z}_2)^3$-actions under these operations....

Abstract We study the topology of small covers from their fundamental groups. find a way to obtain explicit presentations group cover. Then we use these relations between groups cover and its facial submanifolds. In particular, can determine when submanifold is $\pi _1$-injective in terms some purely combinatorial data on underlying simple polytope. addition, that any three-dimensional has an embedded non-simply connected surface. Using this result results Schoen Yau [25], characterize all...

In this paper, we establish the Composition-Diamond lemma for free differential algebras. As applications, give Groebner-Shirshov bases Lie-differential algebra and commutative-differential algebra, respectively.

Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper Y"> <mml:semantics> <mml:mi>Y</mml:mi> <mml:annotation encoding="application/x-tex">Y</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a closed, connected, orientable three-manifold admitting genus one open book decomposition with boundary component. We prove that if is an L-space, then the fundamental group of not left-orderable. This answers question...

In dimension $4$, we show that a nontrivial flat cone cannot be approximated by smooth Ricci shrinkers with bounded scalar curvature and Harnack inequality under the pointed-Gromov-Hausdorff topology. As applications, obtain uniform positive lower bounds of potential functions on satisfying some natural geometric properties.

In this paper, we completely characterize when a group algebra FG of finite abelian G over field F is ∗-clean ring. The main result states that, for order n and Fq with char(Fq) = p, the FqG under classical involution if only there exists positive integer w such that qdw≡−1(modm), where G(p) Sylow p-subgroup G, m exp(G∕G(p)) exponent G∕G(p), m2 second G∕G(p) d q modulo m2. Particularly, Cn cyclic gcd(p,n) 1, then FqCn qw≡−1(modn). Our results improve several known give an answer to existing...

Let A be a brace algebra. This structure implies that is also pre-Lie In this paper, we establish Composition-Diamond lemma for algebras. For each algebra L, find Gröbner–Shirshov basis its universal Ub(L). As applications, determine an explicit linear Ub(L) and prove L subalgebra of

In this paper, by using Gröbner–Shirshov bases theories, we prove that each countably generated associative algebra (Lie algebra) can be embedded into a simple two-generated algebra).

Abstract It is shown that a small cover (resp. real moment-angle manifold) over simple polytope an infra-solvmanifold if and only it diffeomorphic to Bott manifold flat torus). Moreover, we obtain several equivalent conditions for be homeomorphic manifold. In addition, study Riemannian metrics on covers manifolds with certain the Ricci or sectional curvature. We will see these curvature put very strong restrictions topology of corresponding combinatorial structures underlying polytopes.

In this paper, we systematically study the heat kernel of Ricci flows induced by shrinkers. We develop several estimates which are much sharper than their counterparts in general closed flows. Many classical results, including optimal Logarithmic Sobolev constant estimate, no-local-collapsing theorem, pseudo-locality theorem and strong maximum principle for curvature tensors, essentially improved Our results provide many necessary tools to analyze short time singularities dimension.

Abstract In this paper we study the structure of pointed-Gromov–Hausdorff limits sequences Ricci shrinkers. We define a regular-singular decomposition following work Cheeger–Colding for manifolds with uniform curvature lower bound, and prove that regular part any non-collapsing shrinker limit space is strongly convex, inspired by Colding–Naber’s original idea parabolic smoothing distance functions.