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Creators/Authors contains: "Schulze, Felix"

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  1. ; ; (, Inventiones mathematicae)
    Abstract We prove Ilmanen’s resolution of point singularities conjecture by establishing short-time smoothness of the level set flow of a smooth hypersurface with isolated conical singularities. This shows how the mean curvature flow evolves through asymptotically conical singularities. Precisely, we prove that the level set flow of a smooth hypersurface$$M^{n}\subset \mathbb{R}^{n+1}$$ M n ⊂ R n + 1 ,$$2\leq n\leq 6$$ 2 ≤ n ≤ 6 , with an isolated conical singularity is modeled on the level set flow of the cone. In particular, the flow fattens (instantaneously) if and only if the level set flow of the cone fattens. 
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    Free, publicly-accessible full text available December 1, 2025
  2. ; ; ; (, Inventiones mathematicae)
    Abstract We show that the mean curvature flow of generic closed surfaces in$$\mathbb{R}^{3}$$ R 3 avoids asymptotically conical and non-spherical compact singularities. We also show that the mean curvature flow of generic closed low-entropy hypersurfaces in$$\mathbb{R}^{4}$$ R 4 is smooth until it disappears in a round point. The main technical ingredient is a long-time existence and uniqueness result for ancient mean curvature flows that lie on one side of asymptotically conical or compact shrinking solitons. 
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  3. ; ; (, Ars Inveniendi Analytica)
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  4. ; ; (, Publications mathématiques de l'IHÉS)
    Abstract Suppose that ℳ is an almost calibrated, exact, ancient solution of Lagrangian mean curvature flow in$$\mathbf {C} ^{n}$$ C n . We show that if ℳ has a blow-down given by the static union of two Lagrangian subspaces with distinct Lagrangian angles that intersect along a line, then ℳ is a translator. In particular in$$\mathbf {C} ^{2}$$ C 2 , all almost calibrated, exact, ancient solutions of Lagrangian mean curvature flow with entropy less than 3 are special Lagrangian, a union of planes, or translators. 
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  5. ; ; ; (, Duke Mathematical Journal)
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  6. ; (, Duke Mathematical Journal)
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  7. ; ; (, Journal für die reine und angewandte Mathematik (Crelles Journal))
    Abstract A variant of Li–Tam theory, which associates to each end of a completeRiemannian manifold a positive solution of a given Schrödinger equation onthe manifold, is developed. It is demonstrated that such positive solutionsmust be of polynomial growth of fixed order under a suitable scalinginvariant Sobolev inequality. Consequently, a finiteness result for the number of endsfollows. In the case when the Sobolev inequality is of particular type, the finiteness resultis proven directly. As an application, an estimate on the number of ends for shrinkinggradient Ricci solitons and submanifolds of Euclidean space is obtained. 
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