Zobrazeno 1 - 10
of 27
pro vyhledávání: '"Minter, Paul"'
We prove that the singular set of an $m$-dimensional integral current $T$ in $\mathbb{R}^{n + m}$, semicalibrated by a $C^{2, \kappa_0}$ $m$-form $\omega$ is countably $(m - 2)$-rectifiable. Furthermore, we show that there is a unique tangent cone at
Externí odkaz:
http://arxiv.org/abs/2409.03037
We study fine structural properties related to the interior regularity of $m$-dimensional area minimizing currents mod$(q)$ in arbitrary codimension. We show: (i) the set of points where at least one tangent cone is translation invariant along $m-1$
Externí odkaz:
http://arxiv.org/abs/2403.15889
Autor:
Edelen, Nick, Minter, Paul
We establish uniqueness and regularity results for tangent cones (at a point or at infinity) with isolated singularities arising from a given immersed stable minimal hypersurface with suitably small (non-immersed) singular set. In particular, our res
Externí odkaz:
http://arxiv.org/abs/2401.15301
We show that a complete, two-sided, stable minimal hypersurface in $\mathbf{R}^5$ is flat.
Externí odkaz:
http://arxiv.org/abs/2401.01492
We consider an area-minimizing integral current $T$ of codimension higher than 1 ins a smooth Riemannian manifold $\Sigma$. We prove that $T$ has a unique tangent cone, which is a superposition of planes, at $\mathcal{H}^{m-2}$-a.e. point in its supp
Externí odkaz:
http://arxiv.org/abs/2304.11553
Autor:
Minter, Paul
For each positive integer $Q\in\mathbb{Z}_{\geq 2}$, we prove a multi-valued $C^{1,\alpha}$ regularity theorem for varifolds in the class $\mathcal{S}_Q$, i.e., stable codimension one stationary integral $n$-varifolds which have no classical singular
Externí odkaz:
http://arxiv.org/abs/2210.04744
We prove local measure bounds on the tubular neighbourhood of the singular set of codimension one stationary integral $n$-varifolds $V$ in Riemannian manifolds which have both: (i) finite index on their smoothly embedded part; and (ii) $\mathcal{H}^{
Externí odkaz:
http://arxiv.org/abs/2209.11992
Autor:
Minter, Paul, Wickramasekera, Neshan
For any $Q\in\{\frac{3}{2},2,\frac{5}{2},3,\dotsc\}$, we establish a structure theory for the class $\mathcal{S}_Q$ of stable codimension 1 stationary integral varifolds admitting no classical singularities of density $
Externí odkaz:
http://arxiv.org/abs/2111.11202
Autor:
Minter, Paul
The regularity theory of the Campanato space $\mathcal{L}^{(q,\lambda)}_k(\Omega)$ has found many applications within the regularity theory of solutions to various geometric variational problems. Here we extend this theory from single-valued function
Externí odkaz:
http://arxiv.org/abs/2108.03085
Autor:
Minter, Paul
We prove a multi-valued $C^{1,\alpha}$ regularity theorem for the varifolds in the class $\mathcal{S}_2$ (i.e., stable codimension one stationary integral $n$-varifolds admitting no triple junction classical singularities) which are sufficiently clos
Externí odkaz:
http://arxiv.org/abs/2108.02614