Zobrazeno 1 - 10
of 3 253
pro vyhledávání: '"Monotonicity formula"'
The celebrated Almgren monotonicity formula for harmonic functions $u:\mathbb{R}^n \rightarrow \mathbb{R}$ says that its $L^2-$energy concentrated on a sphere of radius $r$, when measured in a suitable sense, is non-decreasing: if $u$ oscillates at a
Externí odkaz:
http://arxiv.org/abs/2311.11887
Autor:
Ferrari, Fausto, Forcillo, Nicolò
Publikováno v:
Boll Unione Mat Ital (2023)
In this paper we provide a different approach to the Alt-Caffarelli-Friedman monotonicity formula, reducing the problem to test the monotone increasing behavior of the mean value of a function involving the norm of the gradient. In particular, we sho
Externí odkaz:
http://arxiv.org/abs/2310.13264
Autor:
Kawai, Kotaro
For Hermitian connections on a Hermitian complex line bundle over a Riemannian manifold, we can define the ``volume", which can be considered to be the ``mirror" of the standard volume for submanifolds. We call the critical points minimal connections
Externí odkaz:
http://arxiv.org/abs/2309.11796
The goal of this paper is to establish a monotonicity formula for perimeter minimizing sets in RCD(0,N) metric measure cones, together with the associated rigidity statement. The applications include sharp Hausdorff dimension estimates for the singul
Externí odkaz:
http://arxiv.org/abs/2307.06205
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Autor:
Fischer, Julian
We establish a new monotonicity formula for minimizers of the Mumford-Shah functional in planar domains. Our formula follows the spirit of Bucur-Luckhaus, but works with the David-L\'eger entropy instead of the energy. Interestingly, this allows for
Externí odkaz:
http://arxiv.org/abs/2203.13177
Autor:
White, Brian
For a manifold-with-boundary moving by mean curvature flow, the entropy at a later time is bounded by the entropy at an earlier time plus a boundary term. This paper controls the boundary term in a geometrically natural way. In particular, it shows (
Externí odkaz:
http://arxiv.org/abs/2204.01983
Publikováno v:
Ars Inveniendi Analytica (2023), Paper No. 1, 49 pp
The objective of this paper is two-fold. First, we establish new sharp quantitative estimates for Faber-Krahn inequalities on simply connected space forms. We prove that the gap between the first eigenvalue of a given set $\Omega$ and that of the bal
Externí odkaz:
http://arxiv.org/abs/2107.03505
Autor:
Rivière, Tristan
We prove an almost monotonicity formula for H-minimal Legendrian Surfaces (also called {\it contact stationary legendrian immersions}) in the Heisenberg Group ${\mathbb H}^2$ . From this formula we deduce a Bernstein-Liouville type theorem for H-mini
Externí odkaz:
http://arxiv.org/abs/2108.09685
Akademický článek
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