• Commun. Anal. Geom. (IF 0.62) Pub Date :
Colin Adams; Gregory Kehne

Generalizing previous constructions, we present a dual pair of decompositions of the complement of a link $L$ into bipyramids, given any multicrossing projection of $L$. When $L$ is hyperbolic, this gives new upper bounds on the volume of $L$ given its multicrossing projection. These bounds are realized by three closely related infinite tiling weaves.

更新日期：2020-07-20
• Commun. Anal. Geom. (IF 0.62) Pub Date :
Sergey I. Agafonov

We study non-flat planar 3‑webs with infinitesimal symmetries. Using multi-dimensional Schwarzian derivative we give a criterion for linearization of such webs and present a projective classification thereof. Using this classification we show that the Gronwall conjecture is true for 3‑webs admitting infinitesimal symmetries.

更新日期：2020-07-20
• Commun. Anal. Geom. (IF 0.62) Pub Date :
R. Batista; M. Ranieri; E. Ribeiro

The purpose of this article is to investigate the structure of complete non-compact quasi-Einstein manifolds. We show that complete noncompact quasi-Einstein manifolds with $\lambda = 0$ are connected at infinity. In addition, we provide some conditions under which quasi-Einstein manifolds with $\lambda \lt 0$ are $f$-non-parabolic. In particular, we obtain estimates on volume growth of geodesic balls

更新日期：2020-07-20
• Commun. Anal. Geom. (IF 0.62) Pub Date :
Der-Chen Chang; Shu-Cheng Chang; Chien Lin

In this paper, we generalize Cao–Yau’s gradient estimate for the sum of squares of vector fields up to higher step under assumption of the generalized curvature-dimension inequality. With its applications, by deriving a curvature-dimension inequality, we are able to obtain the Li–Yau gradient estimate for the CR heat equation in a closed pseudohermitian manifold of nonvanishing torsion tensors. As

更新日期：2020-07-20
• Commun. Anal. Geom. (IF 0.62) Pub Date :
Jason D. Lotay; Tommaso Pacini

We show that the properties of Lagrangian mean curvature flow are a special case of a more general phenomenon, concerning couplings between geometric flows of the ambient space and of totally real submanifolds. Both flows are driven by ambient Ricci curvature or, in the non-Kähler case, by its analogues. To this end we explore the geometry of totally real submanifolds, defining (i) a new geometric

更新日期：2020-07-20
• Commun. Anal. Geom. (IF 0.62) Pub Date :
Giovanni Molica Bisci; Dušan Repovš; Luca Vilasi

By using variational techniques we provide new existence results for Yamabe-type equations with subcritical perturbations set on a compact $d$-dimensional $(d \geq 3)$ Riemannian manifold without boundary. As a direct consequence of our main theorems, we prove the existence of at least one solution to the following Yamabe-type problem\[\begin{cases}-\Delta_g w + \alpha(\sigma) w = \mu K(\sigma) w^{\frac{d+2}{d-2}}

更新日期：2020-07-20
• Commun. Anal. Geom. (IF 0.62) Pub Date :
Miles Simon

We consider solutions $(M^4 , g(t)), 0 \leq t \lt T$, to Ricci flow on compact, four-dimensional manifolds without boundary. We prove integral curvature estimates which are valid for any such solution. In the case that the scalar curvature is bounded and $T \lt \infty$, we show that these estimates imply that the (spatial) integral of the square of the norm of the Riemannian curvature is bounded by

更新日期：2020-07-20
• Commun. Anal. Geom. (IF 0.62) Pub Date :
Zhuhong Zhang

In this paper, we will prove a gap theorem on four-dimensional gradient shrinking soliton. More precisely, we will show that any complete four-dimensional gradient shrinking soliton with nonnegative and bounded Ricci curvature, satisfying a pinched Weyl curvature, either is flat, or $\lambda_1 + \lambda_2 \geq c_0 R \gt 0$ at all points, where $c_0 \approx 0.29167$ and $\lbrace \lambda_i \rbrace$ are

更新日期：2020-07-20
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