Related papers: Marked length pattern rigidity for arithmetic mani…

The main result of this article is a Llarull-type rigidity statement for scalar curvature on Riemannian spin manifolds with cone-like singularities in odd dimensions. The even dimensional analog was proven in an earlier work together with…

We introduce the notion of rigidity for automorphic representations of groups over global function fields. We construct the Langlands parameters of rigid automorphic representations explicitly as local systems over open curves. We expect…

We prove a topological rigidity theorem for closed hypersurfaces of the Euclidean sphere and of an elliptic space form. It asserts that, under a lower bound hypothesis on the absolute value of the principal curvatures, the hypersurface is…

We extend our generic rigidity theory for periodic frameworks in the plane to frameworks with a broader class of crystallographic symmetry. Along the way we introduce a new class of combinatorial matroids and associated linear…

We extend our recent work with K. Zumbrun on long-time stability of multi-dimensional noncharacteristic viscous boundary layers of a class of symmetrizable hyperbolic-parabolic systems. Our main improvements are (i) to establish the…

We derive a necessary and sufficient condition on a hyperplane arrangement in $\mathbb{P}^n$ for the associated logarithmic cotangent bundle to be ample modulo boundary. We extend this result to the orbifold setting and give some…

We determine the adjoint trace field of gluings of general hyperbolic manifolds. This provides a new method to prove the nonarithmeticity of gluings, which can be applied to the classical construction of Gromov and Piatetski-Shapiro (and…

We prove a coherence theorem for invertible objects in a symmetric monoidal category. This is used to deduce associativity, skew-commutativity, and related results for multi-graded morphism rings, generalizing the well-known versions for…

We propose a unified framework in which the different constructions of cohomology groups for topological and Lie groups can all be treated on equal footings. In particular, we show that the cohomology of "locally continuous" cochains…

We establish a sharp upper bound for the bottom spectrum of the Beltrami Laplacian on universal covers of closed Riemannian manifolds with scalar curvature lower bound. Moreover, we prove a scalar curvature rigidity theorem when this bound…

An important, if relatively less well known aspect of the singularity theorems in Lorentzian Geometry is to understand how their conclusions fare upon weakening or suppression of one or more of their hypotheses. Then, theorems with modified…

We consider random perfect matchings on a general class of contracting bipartite graphs by letting certain edge weights be 0 on the contracting square-hexagon lattice in a periodic way. We obtain a deterministic limit shape in the scaling…

We establish a rigidity theorem for Brendle and Hung's recent systolic inequality, which involves Gromov's notion of \(T^{\rtimes}\)-stabilized scalar curvature. Our primary technique is the construction of foliations by free boundary…

In this paper we show that if a linear cocycle is robustly periodical stable then it is uniformly stable.

We develop further basic tools in the theory of continuous bounded cohomology of locally compact groups. We apply this tools to establish a Milnor-Wood type inequality in a very general context and to prove a global rigidity result which…

This paper is the next installment of our analysis of length-commensurable locally symmetric spaces begun in Publ. math. IHES 109(2009), 113-184. For a Riemannian manifold $M$, we let $L(M)$ be the weak length spectrum of $M$, i.e. the set…

We consider the global rigidity problem for bar-joint frameworks where each vertex is constrained to lie on a particular line in $\mathbb R^d$. In our setting we allow multiple vertices to be constrained to the same line. Under a mild…

We prove trivialization of the first cohomology with coefficients in smooth vector fields, for a class of $\mathbb Z^2$ parabolic actions on $(SL(2, \mathbb R)\times SL(2, \mathbb R))/\Gamma$, where the lattice $\Gamma$ is irreducible and…

Let $M$ be a complex $n$-dimensional projective manifold in $\mathbb{P}^{n+r}$ endowed with the Fubini-Study metric of constant holomorphic sectional curvature $1$, $\sigma$ its second fundamental form, and $\underline{|\sigma|}^2$ the mean…

Let $M$ be a compact oriented 3-manifold with non-empty boundary consisting of surfaces of genii $>1$ such that the interior of $M$ is hyperbolizable. We show that for each spherical cone-metric $d$ on $\partial M$ such that all cone-angles…