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pro vyhledávání: '"Mantoulidis A"'
Bamler--Kleiner recently proved a multiplicity-one theorem for mean curvature flow in $\mathbb{R}^3$ and combined it with the authors' work on generic mean curvature flows to fully resolve Huisken's genericity conjecture. In this paper we show that a
Externí odkaz:
http://arxiv.org/abs/2409.01463
We prove that the mean curvature flow of a generic closed embedded hypersurface in $\mathbb{R}^4$ or $\mathbb{R}^5$ with entropy $\leq 2$, or with entropy $\leq \lambda(\mathbb{S}^1)$ if in $\mathbb{R}^6$, encounters only generic singularities.
Externí odkaz:
http://arxiv.org/abs/2309.03856
Publikováno v:
Ars Inveniendi Analytica (2024), Paper No. 3, 15 pp
Let $\Gamma$ be a smooth, closed, oriented, $(n-1)$-dimensional submanifold of $\mathbb{R}^{n+1}$. We show that there exist arbitrarily small perturbations $\Gamma'$ of $\Gamma$ with the property that minimizing integral $n$-currents with boundary $\
Externí odkaz:
http://arxiv.org/abs/2306.13191
We prove that singularities of area minimizing hypersurfaces can be perturbed away in ambient dimensions 9 and 10.
Comment: Minor revisions. All comments welcome
Comment: Minor revisions. All comments welcome
Externí odkaz:
http://arxiv.org/abs/2302.02253
Autor:
Lukas Junk, Volker M. Schmiedel, Somraj Guha, Katharina Fischel, Peter Greb, Kristin Vill, Violetta Krisilia, Lasse van Geelen, Klaus Rumpel, Parvinder Kaur, Ramya V. Krishnamurthy, Shridhar Narayanan, Radha Krishan Shandil, Mayas Singh, Christiane Kofink, Andreas Mantoulidis, Philipp Biber, Gerhard Gmaschitz, Uli Kazmaier, Anton Meinhart, Julia Leodolter, David Hoi, Sabryna Junker, Francesca Ester Morreale, Tim Clausen, Rainer Kalscheuer, Harald Weinstabl, Guido Boehmelt
Publikováno v:
Nature Communications, Vol 15, Iss 1, Pp 1-15 (2024)
Abstract Antimicrobial resistance is a global health threat that requires the development of new treatment concepts. These should not only overcome existing resistance but be designed to slow down the emergence of new resistance mechanisms. Targeted
Externí odkaz:
https://doaj.org/article/762402cfc91745d09f200167975e5d00
Autor:
Mantoulidis, Christos
In this short note we see that double-well phase transitions exhibit more rigidity than their minimal hypersurface counterparts.
Comment: 9 pages. To appear in the Proceedings of the AMS
Comment: 9 pages. To appear in the Proceedings of the AMS
Externí odkaz:
http://arxiv.org/abs/2208.00582
We show that every closed, oriented, topologically PSC 4-manifold can be obtained via 0 and 1-surgeries from a topologically PSC 4-orbifold with vanishing first Betti number and second Betti number at most as large as the original one.
Comment:
Comment:
Externí odkaz:
http://arxiv.org/abs/2206.09335
Autor:
Chodosh, Otis, Mantoulidis, Christos
The $p$-widths of a closed Riemannian manifold are a nonlinear analogue of the spectrum of its Laplace--Beltrami operator, which corresponds to areas of a certain min-max sequence of possibly singular minimal submanifolds. We show that the $p$-widths
Externí odkaz:
http://arxiv.org/abs/2107.11684
Autor:
Li, Chao, Mantoulidis, Christos
On a closed manifold, consider the space of all Riemannian metrics for which -Delta + kR is positive (nonnegative) definite, where k > 0 and R is the scalar curvature. This spectral generalization of positive (nonnegative) scalar curvature arises nat
Externí odkaz:
http://arxiv.org/abs/2106.15709
We prove that sufficiently low-entropy closed hypersurfaces can be perturbed so that their mean curvature flow encounters only spherical and cylindrical singularities. Our theorem applies to all closed surfaces in $\mathbb{R}^3$ with entropy $\leq 2$
Externí odkaz:
http://arxiv.org/abs/2102.11978