Zobrazeno 1 - 10
of 74
pro vyhledávání: '"Holopainen Ilkka"'
Publikováno v:
Analysis and Geometry in Metric Spaces, Vol 10, Iss 1, Pp 31-39 (2022)
Assuming that there exists a translating soliton u∞ with speed C in a domain Ω and with prescribed contact angle on ∂Ω, we prove that a graphical solution to the mean curvature flow with the same prescribed contact angle converges to u∞ + Ct
Externí odkaz:
https://doaj.org/article/eaf81484258d438a8e888a05a7c74dba
We construct a blowing-up solution for the energy critical focusing biharmonic nonlinear Schr\"odinger equation in infinite time in dimension $N\geq 13$. Our solution is radially symmetric and converges asymptotically to the sum of two bubbles. The s
Externí odkaz:
http://arxiv.org/abs/2304.14744
We study the fourth order Schr\"odinger equation with mixed dispersion on an $N$-dimensional Cartan-Hadamard manifold. At first, we focus on the case of the hyperbolic space. Using the fact that there exists a Fourier transform on this space, we prov
Externí odkaz:
http://arxiv.org/abs/2105.13804
Publikováno v:
Analysis and Geometry in Metric Spaces, vol. 10, no. 1, 2022, pp. 31-39
Assuming that there exists a translating soliton $u_\infty$ with speed $C$ in a domain $\Omega$ and with prescribed contact angle on $\partial\Omega$, we prove that a graphical solution to the mean curvature flow with the same prescribed contact angl
Externí odkaz:
http://arxiv.org/abs/2007.03928
Publikováno v:
The Journal of Geometric Analysis 33, 163 (2023)
We prove existence results for entire graphical translators of the mean curvature flow (the so-called bowl solitons) on Cartan-Hadamard manifolds. We show that the asymptotic behaviour of entire solitons depends heavily on the curvature of the manifo
Externí odkaz:
http://arxiv.org/abs/2007.02989
Publikováno v:
Proc. Amer. Math. Soc. 148 (2020), 1731-1743
We prove the existence of solutions to the asymptotic Plateau problem for hypersurfaces of prescribed mean curvature in Cartan-Hadamard manifolds $N$. More precisely, given a suitable subset $L$ of the asymptotic boundary of $N$ and a suitable functi
Externí odkaz:
http://arxiv.org/abs/1903.11111
We study the asymptotic Dirichlet problem for Killing graphs with prescribed mean curvature $H$ in warped product manifolds $M\times_\varrho \mathbb{R}$. In the first part of the paper, we prove the existence of Killing graphs with prescribed boundar
Externí odkaz:
http://arxiv.org/abs/1801.04210
Publikováno v:
Proc. Roy. Soc. Edinburgh Sect. A 150 (2020), 341-366
We prove that every entire solution of the minimal graph equation that is bounded from below and has at most linear growth must be constant on a complete Riemannian manifold $M$ with only one end if $M$ has asymptotically non-negative sectional curva
Externí odkaz:
http://arxiv.org/abs/1701.00953
We study the asymptotic Dirichlet problem for $f$-minimal graphs in Cartan-Hadamard manifolds $M$. $f$-minimal hypersurfaces are natural generalizations of self-shrinkers which play a crucial role in the study of mean curvature flow. In the first par
Externí odkaz:
http://arxiv.org/abs/1605.01935
Publikováno v:
Math. Z. 290 (2018), 221-250
We study the asymptotic Dirichlet and Plateau problems on Cartan-Hadamard manifolds satisfying the so-called Strict Convexity (abbr. SC) condition. The main part of the paper consists in studying the SC condition on a manifold whose sectional curvatu
Externí odkaz:
http://arxiv.org/abs/1507.07311