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We use the Weil–Petersson gradient flow for renormalized volume to study the space CC(N;S,X) of convex cocompact hyperbolic structures on the relatively acylindrical 3-manifold (N;S). Among the cases of interest are the deformation space of an acylindrical manifold and the Bers slice of quasifuchsian space associated to a fixed surface. To treat the possibility of degeneration along flow-lines to peripherally cusped structures, we introduce a surgery procedure to yield a surgered gradient flow that limits to the unique structure M_geod in CC( N;S,X) with totally geodesic convex core boundary facing S. Analyzing the geometry of structures along a flow line, we show that if V_R(M) is the renormalized volume of M, then V_R(M)−V_R(M_geod) is bounded below by a linear function of the Weil Petersson distance d_WP(∂_c M,∂_cM_geod), with constants depending only on the topology of S. The surgered flow gives a unified approach to a number of problems in the study of hyperbolic 3-manifolds, providing new proofs and generalizations of well-known theorems such as Storm’s result that M geod has minimal volume for N acylindrical and the second author’s result comparing convex core volume and Weil–Petersson distance for quasifuchsian manifolds. 

Novel noncollinear antiferromagnets with spontaneous time-reversal symmetry breaking, nontrivial band topology, and unconventional transport properties have received immense research interest over the past decade due to their rich physics and enormous promise in technological applications. One of the central focuses in this emerging field is exploring the relationship between the microscopic magnetic structure and exotic material properties. Here, the nanoscale imaging of both spin-orbit-torque-induced deterministic magnetic switching and chiral spin rotation in noncollinear antiferromagnet Mn3Sn films using nitrogen-vacancy (NV) centers is reported. Direct evidence of the off-resonance dipole-dipole coupling between the spin dynamics in Mn3Sn and proximate NV centers is also demonstrated with NV relaxometry measurements. These results demonstrate the unique capabilities of NV centers in accessing the local information of the magnetic order and dynamics in these emergent quantum materials and suggest new opportunities for investigating the interplay between topology and magnetism in a broad range of topological magnets. 

In this paper, we construct examples of Weil–Petersson geodesics with nonminimal ending laminations which have [Formula: see text]-dimensional limit sets in the Thurston compactification of Teichmüller space. 

Abstract Given a sequence of curves on a surface, we provide conditions which ensure that (1) the sequence is an infinite quasi-geodesic in the curve complex, (2) the limit in the Gromov boundary is represented by a nonuniquely ergodic ending lamination, and (3) the sequence divides into a finite set of subsequences, each of which projectively converges to one of the ergodic measures on the ending lamination. The conditions are sufficiently robust, allowing us to construct sequences on a closed surface of genus g for which the space of measures has the maximal dimension {3g-3} , for example. We also study the limit sets in the Thurston boundary of Teichmüller geodesic rays defined by quadratic differentials whose vertical foliations are obtained from the constructions mentioned above. We prove that such examples exist for which the limit is a cycle in the 1-skeleton of the simplex of projective classes of measures visiting every vertex. 

Abstract In this paper we prove that the limit set of any Weil–Petersson geodesic ray with uniquely ergodic ending lamination is a single point in the Thurston compactification of Teichmüller space. On the other hand, we construct examples of Weil–Petersson geodesics with minimal non-uniquely ergodic ending laminations and limit set a circle in the Thurston compactification.