https://neckpinch.com/authors/niels-martin-moller/New arXiv papers by Niels Martin Møller, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2509.11473/arxiv:2509.11473Sun, 14 Sep 2025 00:00:00 GMTEddygledson Souza Gama, Francisco Martín, Niels Martin Møller — We show that mean curvature flow translators may exhibit non-removable singularities at infinity, due to jump discontinuities in their asymptotic profiles, and that oscillation can persist so as to yield a continuum of subsequential limit tangent planes. Nonetheless, we prove that as time t→± ∞, any finite entropy, finite genus, embedded, collapsed translating soliton in ℝ³ converges to a uniquely determined collection of planes. This requires global analysis of quasilinear soliton equations with non-perturbative drifts, which we analyze via sharp non-standard elliptic decay estimates for the drift Laplacian, implying improvements on the Evans-Spruck and Ecker-Huisken estimates in the soliton setting, and exploiting a link from potential theory of the Yukawa equation to heat flows with L^∞-data on non-compact slice curves of these solitons. The structure theorem follows: such solitons decompose at infinity into standard regions asymptotic to planes or grim reaper cylinders. As one application, we classify collapsed translators of entropy two with empty limits as t→ +∞.Mean curvature flowSelf-shrinkers & translatorsSingularitiesStability & uniquenessBoundaries & non-compact https://neckpinch.com/papers/2209.01640/arxiv:2209.01640Sun, 04 Sep 2022 00:00:00 GMTEddygledson Souza Gama, Francisco Martín, Niels Martin Møller — We study translating solitons for the mean curvature flow, Σ²⊆ℝ³ which are contained in slabs, and are of finite genus and finite entropy. As a first consequence of our results, we can enumerate connected components of slices to define asymptotic invariants ω^±(Σ)∈ℕ, which count the numbers of "wings". Analyzing these, we give a method for computing the entropies λ(Σ) via a simple formula involving the wing numbers, which in particular shows that for this class of solitons the entropy is quantized into integer steps. Finally, combining the concept of wing numbers with Morse theory for minimal surfaces, we prove the uniqueness theorem that if Σ is a complete embedded simply connected translating soliton contained in a slab with entropy λ(Σ)=3 and containing a vertical line, then Σ is one of the translating pitchforks of Hoffman-Martín-WhiteMean curvature flowSelf-shrinkers & translatorsStability & uniquenessMinimal & CMC surfaces