Asymptotic Criticality of the Navier-Stokes Regularity Problem
November 3, 2019
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Mathematics
Physics
Analysis of PDEs
Mathematical Physics
Mathematical Physics
Analysis of PDEs
Mathematical Physics
Mathematical Physics
The problem of global-in-time regularity for the 3D Navier-Stokes equations,
i.e., the question of whether a smooth flow can exhibit spontaneous formation
of singularities, is a fundamental open problem in mathematical physics. Due to
the s...
Graded Lie algebras of maximal class of type n
November 3, 2019
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Mathematics
Rings and Algebras
Rings and Algebras
Let n>1 be an integer. The algebras of the title, which we abbreviate as
algebras of type n, are infinite-dimensional graded Lie algebras L=⨁i=1∞Li, which are generated by an element of degree 1
and an element o...
A discrete version of Liouville's theorem on conformal maps
November 3, 2019
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Mathematics
Differential Geometry
Combinatorics
Complex Variables
Geometric Topology
Differential Geometry
Combinatorics
Complex Variables
Geometric Topology
Liouville's theorem says that in dimension greater than two, all conformal
maps are M\"obius transformations. We prove an analogous statement about
simplicial complexes, where two simplicial complexes are considered discretely
conformally e...
Homotopy of product systems and K-theory of Cuntz-Nica-Pimsner algebras
November 3, 2019
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Mathematics
Operator Algebras
We introduce the notion of a homotopy of product systems, and show that the
Cuntz-Nica-Pimsner algebras of homotopic product systems over N^k have
isomorphic K-theory. As an application, we give a new proof that the K-theory
of a 2-graph C*...
Continuous and coherent actions on wrapped Fukaya categories
November 1, 2019
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Mathematics
Symplectic Geometry
Algebraic Topology
We establish the continuous functoriality of wrapped Fukaya categories with
respect to Liouville automorphisms, yielding a way to probe the homotopy type
of the automorphism group of a Liouville sector. These methods prove Liouville
and mon...
Convergence of a damped Newton's method for discrete Monge-Ampere
functions with a prescribed asymptotic cone
November 1, 2019
Mathematics
Computer Science
Numerical Analysis
Numerical Analysis
We prove the convergence of a damped Newton's method for the nonlinear system
resulting from a discretization of the second boundary value problem for the
Monge-Ampere equation. The boundary condition is enforced through the use of
the noti...
Entropy-stable positivity-preserving DG schemes for Boltzmann-Poisson
models of collisional electronic transport along energy bands
November 1, 2019
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Mathematics
Computer Science
Physics
Numerical Analysis
Numerical Analysis
Computational Physics
This work is related to developing entropy-stable positivity-preserving
Discontinuous Galerkin (DG) methods as a computational scheme for
Boltzmann-Poisson systems modeling the probability density of collisional
electronic transport along s...
The second boundary value problem for a discrete Monge-Ampere equation
October 31, 2019
Mathematics
Computer Science
Numerical Analysis
Numerical Analysis
In this work we propose a discretization of the second boundary condition for
the Monge-Ampere equation arising in geometric optics and optimal transport.
The discretization we propose is the natural generalization of the popular
Oliker-Pru...
Spectral gap of scl in graphs of groups and 3-manifolds
October 30, 2019
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Mathematics
Geometric Topology
Group Theory
Stable commutator length scl_G(g) of an element g in a group G is an
invariant for group elements sensitive to the geometry and dynamics of G.
For any group G acting on a tree, we prove a sharp bound scl_G(g)>=1/2 for
any g acting without...
Superconvergence of differential structure for finite element methods on
perturbed surface meshes
October 30, 2019
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Mathematics
Computer Science
Numerical Analysis
Numerical Analysis
Differential Geometry
Superconvergence of differential structure on discretized surfaces is studied
in this paper. The newly introduced geometric supercloseness provides us with a
fundamental tool to prove the superconvergence of gradient recovery on deviated
su...