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of 17
pro vyhledávání: '"Assimos, Renan"'
By introducing a more flexible notion of convexity, we obtain a new Omori-Yau maximum principle for harmonic maps. In the spirit of the Calabi-Yau conjectures, this principle is more suitable for studying the unboundedness of certain totally geodesic
Externí odkaz:
http://arxiv.org/abs/2404.08781
We prove the local Lipschitz continuity of sub-elliptic harmonic maps between certain singular spaces, more specifically from the $n$-dimensional Heisenberg group into $CAT(0)$ spaces. Our main theorem establishes that these maps have the desired Lip
Externí odkaz:
http://arxiv.org/abs/2312.17112
Inspired by the halfspace theorem for minimal surfaces in $\mathbb{R}^3$ of Hoffman-Meeks, the halfspace theorem of Rodriguez-Rosenberg, and the cone theorem of Omori, we derive new non-existence results for proper harmonic maps into perturbed cones
Externí odkaz:
http://arxiv.org/abs/2312.12375
Publikováno v:
Calculus of Variations and Partial Differential Equations 62, Article number: 12 (2023)
We consider the graphical mean curvature flow of strictly area decreasing maps $f:M\to N$, where $M$ is a compact Riemannian manifold of dimension $m>1$ and $N$ a complete Riemannian surface of bounded geometry. We prove long-time existence of the fl
Externí odkaz:
http://arxiv.org/abs/2201.05523
Autor:
Assimos, Renan
It is known since the work of Frankel that two compactly immersed minimal hypersurfaces in a manifold with positive Ricci curvature must have an intersection point. Several generalizations of this result can be found in the literature, for example in
Externí odkaz:
http://arxiv.org/abs/2004.08358
Akademický článek
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Autor:
Assimos, Renan, Jost, Jürgen
We relate the existence problem of harmonic maps into $S^2$ to the convex geometry of $S^2$. On one hand, this allows us to construct new examples of harmonic maps of degree 0 from compact surfaces of arbitrary genus into $S^2$. On the other hand, we
Externí odkaz:
http://arxiv.org/abs/1910.13966
Autor:
Assimos, Renan, Jost, Jürgen
A result of B.Solomon (On the Gauss map of an area-minimizing hypersurface. 1984. Journal of Differential Geometry, 19(1), 221-232.) says that a compact minimal hypersurface $M^k$ of the sphere $S^{k+1}$ with $H^1(M)=0$, whose Gauss map omits a neigh
Externí odkaz:
http://arxiv.org/abs/1910.14445
Autor:
Assimos, Renan, Jost, Jürgen
Moser's Bernstein theorem \cite{moser61} says that an entire minimal graph of codimension 1 with bounded slope must be a hyperplane. An analogous result for arbitrary codimension is not true, by an example of Lawson-Osserman. Here, we show that Moser
Externí odkaz:
http://arxiv.org/abs/1811.09869
Akademický článek
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