Browsing by Author "Saez Trumper, Mariel Ines Aura"

Now showing 1 - 7 of 7
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    Haciendo género con pizarras: aportes de la antropología simétrica al estudio del género en la investigación matemática
    (2023) Fernando Valenzuela; María Isabel Cortéz; Saez Trumper, Mariel Ines Aura
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    Short‐time existence for the network flow
    (2023) Jorge Lira; Rafe Mazzeo; Alessandra Pluda; Saez Trumper, Mariel Ines Aura
    This paper contains a new proof of the short‐time existence for the flow by curvature of a network of curves in the plane. Appearing initially in metallurgy and as a model for the evolution of grain boundaries, this flow was later treated by Brakke using varifold methods. There is good reason to treat this problem by a direct PDE approach, but doing so requires one to deal with the singular nature of the PDE at the vertices of the network. This was handled in cases of increasing generality by Bronsard‐Reitich, Mantegazza‐Novaga‐Tortorelli and eventually, in the most general case of irregular networks by Ilmanen‐Neves‐Schulze. Although the present paper proves a result similar to the one in Ilmanen et al., the method here provides substantially more detailed information about how an irregular network “resolves” into a regular one. Either approach relies on the existence of self‐similar expanding solutions found in Mazzeo and Saez. As a precursor to the main theorem, we also prove an unexpected regularity result for the mixed Cauchy‐Dirichlet boundary problem for the linear heat equation on a manifold with boundary.
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    THE HADAMARD FORMULA AND THE RAYLEIGH-FABER-KRAHN INEQUALITY FOR NONLOCAL EIGENVALUE PROBLEMS
    (2022) Benguria, R.D.; Pereira, M.C.; Saez Trumper, Mariel Ines Aura
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    The Hadamard formula for nonlocal eigenvalue problems
    (2023) Rafael D. Benguria; Marcone C. Pereira; Saez Trumper, Mariel Ines Aura
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    THE MEAN CURVATURE FLOW ON SOLVMANIFOLDS
    (2023) Arroyo, R.M.; Ovando, G.P.; Perales, R.; Saez Trumper, Mariel Ines Aura
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    Uniqueness of entire graphs evolving by mean curvature flow
    (2022) Panagiota Daskalopoulos; Saez Trumper, Mariel Ines Aura
    Abstract In this paper we study the uniqueness of graphical mean curvature flow with locally Lipschitz initial data. We first prove that rotationally symmetric entire graphs are unique, without any further assumptions. Our methods also give an alternative simple proof of uniqueness in the one-dimensional case. In the general case, we establish the uniqueness of entire proper graphs that satisfy a uniform lower bound on the second fundamental form. The latter result extends to initial conditions that are proper graphs over subdomains of ℝ n {\mathbb{R}^{n}} . A consequence of our result is the uniqueness of convex entire graphs, which allow us to prove that Hamilton’s Harnack estimate holds for mean curvature flow solutions that are convex entire graphs.
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    UNIQUENESS OF SEMIGRAPHICAL TRANSLATORS
    (2023) Martín, F.; Saez Trumper, Mariel Ines Aura; Tsiamis, R.