dg.differential geometry – A strong form of Mostow rigidity without geometrization?

Gabai proved that homotopy hyperbolic 3-manifolds are virtually hyperbolic, in the paper of that name:

Gabai, David, Homotopy hyperbolic 3-manifolds are virtually
hyperbolic.
J. Amer. Math. Soc. 7 (1994), no. 1, 193–198.

I suspect this is the best you can do without geometrisation.

probability theory – Criteria for the rigidity of the sequence of distribution functions

Leave $$φ_n$$ Be a sequence of characteristic functions. We know that converge at each point of a not empty
open interval around 0
yet function $$φ$$ which is also continued at 0.

Can you say that the sequence
of the distribution functions corresponding to $$φ_n$$They are tight

I am aware of the test of a different version where convergence occurs in the entire real line. But what to do in this case?

differential equations – Non-autonomous ODE uses NDSolve, error: Step Size is effectively zero; The singularity or rigidity of the system is suspected.

I have seen this error `NDSolve :: ndsz` many times when I use `NDSolve` To obtain the solution of a non-autonomous ODE. I try but everything has failed. Thanks, Here is the code, very simple.

``````    s = NDSolve[{x'
Y
X[0] == 1, and[0] == 1}, {x
``````