Global solutions of the Euler–Maxwell two-fluid system in 3D
The fundamental “two-fluid” model for describing plasma dynamics is given by the Euler–Maxwell system, in which compressible ion and electron fluids interact with their own self-consistent...
View ArticleRegularity of area minimizing currents II: center manifold
This is the second paper of a series of three on the regularity of higher codimension area minimizing integral currents. Here we perform the second main step in the analysis of the singularities,...
View ArticleRegularity of area minimizing currents III: blow-up
This is the last of a series of three papers in which we give a new, shorter proof of a slightly improved version of Almgren’s partial regularity of area minimizing currents in Riemannian manifolds....
View ArticlePerverse sheaves over real hyperplane arrangements
Let $\mathcal{H}$ be an arrangement of real hyperplanes in $\mathbb{R}^n$. The complexification of $\mathcal{H}$ defines a natural stratification of $\mathbb{C}^n$. We denote by...
View ArticleSplitting mixed Hodge structures over affine invariant manifolds
We prove that affine invariant manifolds in strata of flat surfaces are algebraic varieties. The result is deduced from a generalization of a theorem of Möller. Namely, we prove that the image of a...
View ArticleEmbedded self-similar shrinkers of genus $0$
We confirm a well-known conjecture that the round sphere is the only compact, embedded self-similar shrinking solution of mean curvature flow in $\mathbb{R}^3$ with genus $0$. More generally, we show...
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