Zobrazeno 1 - 10
of 3 196
pro vyhledávání: '"53a10"'
Autor:
Kaya, Seher, López, Rafael
Spacelike intrinsic rotational surfaces with constant mean curvature in the Lorentz-Minkowski space $\E_1^3$ have been recently investigated by Brander et al., extending the known Smyth's surfaces in Euclidean space. Assuming that the surface is intr
Externí odkaz:
http://arxiv.org/abs/2411.19499
Autor:
López, Rafael
We introduce the Frenet theory of curves in dual space $\d^3$. After defining the curvature and the torsion of a curve, we classify all curves in dual plane with constant curvature. We also establish the fundamental theorem of existence in the theory
Externí odkaz:
http://arxiv.org/abs/2411.19494
S-embeddings were introduced by Chelkak as a tool to study the conformal invariance of the thermodynamic limit of the Ising model. Moreover, Chelkak, Laslier and Russkikh introduced a lift of s-embeddings to Lorentz space, and showed that in the limi
Externí odkaz:
http://arxiv.org/abs/2411.19055
We introduce the Loop Weierstrass Representation for minimal surfaces in Euclidean space and constant mean curvature 1 surfaces in hyperbolic space by applying integral system methods to the Weierstrass and Bryant representations. We unify associated
Externí odkaz:
http://arxiv.org/abs/2411.04626
Autor:
Seemungal, Luca, Sharp, Ben
We prove a linear upper bound on the Morse index of closed constant mean curvature (CMC) surfaces in orientable three-manifolds in terms of genus, number of branch points and a Willmore-type energy.
Comment: 18 pages
Comment: 18 pages
Externí odkaz:
http://arxiv.org/abs/2411.02932
Autor:
Tinaglia, Giuseppe, Zhou, Alex
In this paper we study the geometry of complete constant mean curvature (CMC) hypersurfaces immersed in an (n + 1)-dimensional Riemannian manifold N (n = 2, 3 and 4) with sectional curvatures uniformly bounded from below. We generalise radius estimat
Externí odkaz:
http://arxiv.org/abs/2411.02151
Autor:
Espinar, José M., Marín, Diego A.
In this paper, we study domains $\Omega \subset \mathbb{S}^2$ that support positive solutions to the overdetermined problem $ \Delta{u} + f(u, |\nabla u|) = 0 $ in $\Omega$, with the boundary conditions $u = 0$ on $\partial \Omega$ and $|\nabla u|$ b
Externí odkaz:
http://arxiv.org/abs/2410.23777
Autor:
Nandakumaran, Vishnu
Caffarelli-Hardt-Simon used the minimal surface equation on the Simons cone $C(S^3\times S^3)$ to generate newer examples of minimal hypersurfaces with isolated singularities. Hardt-Simon proved that every area-minimizing quadratic cone $\mathcal{C}$
Externí odkaz:
http://arxiv.org/abs/2410.22795
In this paper, we consider the existence of constant mean curvature hypersurfaces with prescribed gradient image. Let $\Omega$ and $\tilde{\Omega}$ be uniformly convex bounded domains in $\mathbb{R}^n$ with smooth boundary. We show that there exists
Externí odkaz:
http://arxiv.org/abs/2411.00817
Autor:
Cho, Joseph, Hara, Masaya
We give a comprehensive account of zero mean curvature surfaces in isotropic 3-space with planar curvature lines. After giving a complete classification all such surfaces, we show that they belong to a 1-parameter family of surfaces. We then investig
Externí odkaz:
http://arxiv.org/abs/2410.18728