Zobrazeno 1 - 10
of 1 521
pro vyhledávání: '"58E20"'
We study a generalization of the manifold-valued Rudin-Osher-Fatemi (ROF) model, which involves an initial datum $f$ mapping from a curved compact surface with smooth boundary to a complete, connected and smooth $n$-dimensional Riemannian manifold. W
Externí odkaz:
http://arxiv.org/abs/2411.19166
We establish universality of the renormalised energy for mappings from a planar domain to a compact manifold, by approximating subquadratic polar convex functionals of the form $\int_\Omega f(|\mathrm{D} u|)\,\mathrm{d} x$. The analysis relies on the
Externí odkaz:
http://arxiv.org/abs/2411.17520
Autor:
Badran, Marco
In a closed, oriented ambient manifold $(M^n,g)$ we consider the problem of finding $\mathbb{S}^1$-valued harmonic maps with prescribed singular set. We show that the boundary of any oriented $(n-1)$-submanifold can be realised as the singular set of
Externí odkaz:
http://arxiv.org/abs/2411.14186
Autor:
Ueno, Ryu
The tension field of the identity map from a statistical manifold to a Riemannian statistical manifold, which shares the same Riemannian metric, is the Tchevychev vector field multiplied by negative one. We derive a new class of statistical manifolds
Externí odkaz:
http://arxiv.org/abs/2411.14156
Autor:
Emam, Christian El, Sagman, Nathaniel
We prove that, on the $\mathrm{SL}(3,\mathbb R)$ Hitchin component, the Goldman symplectic form and the Labourie-Loftin complex structure are compatible and together determine a (mapping class group invariant) pseudo-K\"ahler structure.
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Externí odkaz:
http://arxiv.org/abs/2411.02350
Autor:
Muñoz-Thon, Sebastián
We study a version of Calder\'on's problem for harmonic maps between Riemannian manifolds. By using the higher linearization method, we first show that the Dirichlet-to-Neumann map determines the metric on the domain up to a natural gauge in three ca
Externí odkaz:
http://arxiv.org/abs/2411.01659
Autor:
Munn, Thomas Jack, Riedler, Oskar
In this note we study $(\lambda,\mu)$-eigenfamilies on compact Riemannian manifolds when $\lambda = \mu$. We show that any compact manifold admitting a $(\lambda,\lambda)$-eigenfunction is a mapping torus and that any $(\lambda,\lambda)$-eigenfamily
Externí odkaz:
http://arxiv.org/abs/2409.16932
We prove that harmonic maps into Euclidean buildings, which are not necessarily locally finite, have singular sets of Hausdorff codimension 2, extending the locally finite regularity result of Gromov and Schoen. As an application, we prove superrigid
Externí odkaz:
http://arxiv.org/abs/2408.02783
Each homeomorphic parametrization of a Jordan curve via the unit circle extends to a homeomorphism of the entire plane. It is a natural question to ask if such a homeomorphism can be chosen so as to have some Sobolev regularity. This prompts the simp
Externí odkaz:
http://arxiv.org/abs/2408.00506
We define and study the harmonic curves on domains in $\mathbb{R}^n$ into the first Heisenberg group $\mathbb{H}^1$. These are the $C^2$-regular mappings which are critical points of the second Dirichlet energy and satisfy the weak isotropicity condi
Externí odkaz:
http://arxiv.org/abs/2407.20029