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pro vyhledávání: '"Kleene, Stephen. J."'
Autor:
Kleene, Stephen. J.
In this article, we construct complete embedded constant mean curvature surfaces in $\mb{R}^3$ with freely prescribed genus and any number of ends greater than or equal to four. Heuristically, the surfaces are obtained by resolving finitely many poin
Externí odkaz:
http://arxiv.org/abs/2309.08344
Autor:
Kleene, Stephen J.
In this article, we solve the constant mean curvature dirichlet problem on catenoidal necks with small scale in $\mb{R}^3$. The solutions are found in exponentially weighted H\"older spaces with non-integer weight and are a-priori bounded by a unifor
Externí odkaz:
http://arxiv.org/abs/2308.04257
Autor:
Kleene, Stephen J.
We construct minimal laminations with prescribed singularities on a line segment using perturbation techniques and PDE methods. In addition to the singular set, the rate of curvature blowup is also prescribable in our construction, and we show that a
Externí odkaz:
http://arxiv.org/abs/1410.3183
For fixed large genus, we construct families of complete immersed minimal surfaces in R3 with four ends and dihedral symmetries. The families exist for all large genus and at an appropriate scale degenerate to the plane.
Comment: 45 page, 1 figu
Comment: 45 page, 1 figu
Externí odkaz:
http://arxiv.org/abs/1409.8381
Autor:
Breiner, Christine, Kleene, Stephen J.
We construct helicoid-like embedded minimal disks with axes along self-similar curves modeled on logarithmic spirals. The surfaces have a self-similarity inherited from the curves and the nature of the construction. Moreover, inside of a "logarithmic
Externí odkaz:
http://arxiv.org/abs/1404.6996
Autor:
Breiner, Christine, Kleene, Stephen J.
We use elementary methods to construct a minimal lamination of the interior of a positive cone in R3.
Comment: A few typos fixed. Title changed to reflect more standard terminology
Comment: A few typos fixed. Title changed to reflect more standard terminology
Externí odkaz:
http://arxiv.org/abs/1311.7102
Autor:
Drugan, Gregory, Kleene, Stephen J.
We construct infinitely many complete, immersed self-shrinkers with rotational symmetry for each of the following topological types: the sphere, the plane, the cylinder, and the torus.
Externí odkaz:
http://arxiv.org/abs/1306.2383
Publikováno v:
J. Reine Angew. Math. 739 (2018), 1--39. MR3808256
We give the first rigorous construction of complete, embedded self-shrinking hypersurfaces under mean curvature flow, since Angenent's torus in 1989. The surfaces exist for any sufficiently large prescribed genus $g$, and are non-compact with one end
Externí odkaz:
http://arxiv.org/abs/1106.5454
Publikováno v:
Trans. Amer. Math. Soc. 366 (2014), no. 8, 3943--3963. MR3206448
In this paper we present a new family of non-compact properly embedded, self-shrinking, asymptotically conical, positive mean curvature ends $\Sigma^n\subseteq\mathbb{R}^{n+1}$ that are hypersurfaces of revolution with circular boundaries. These hype
Externí odkaz:
http://arxiv.org/abs/1008.1609
Autor:
Kleene, Stephen J.
Given a compact closed subset $M$ of a line segment in $\mathbb{R}^3$, we construct a sequence of minimal surfaces $\Sigma_k$ embedded in a neighborhood $C$ of the line segment that converge smoothly to a limit lamination of $C$ away from $M$. Moreov
Externí odkaz:
http://arxiv.org/abs/0910.0199