Zobrazeno 1 - 10
of 546
pro vyhledávání: '"53A07"'
Autor:
Raffaelli, Matteo
Given a smooth $s$-dimensional submanifold $S$ of $\mathbb{R}^{m+c}$ and a smooth distribution $\mathcal{D}\supset TS$ of rank $m$ along $S$, we study the following geometric Cauchy problem: to find an $m$-dimensional rank-$s$ submanifold $M$ of $\ma
Externí odkaz:
http://arxiv.org/abs/2409.04358
Autor:
Bayard, Pierre, Seppi, Andrea
We show that every regular domain $\mathcal D$ in Minkowski space $\mathbb R^{n,1}$ which is not a wedge admits an entire hypersurface whose domain of dependence is $\mathcal D$ and whose scalar curvature is a prescribed constant (or function, under
Externí odkaz:
http://arxiv.org/abs/2408.10042
Autor:
Petrunin, Anton
Suppose M is a closed submanifold in a Euclidean ball of large dimension. We give an optimal bound on the normal curvatures that guarantee that M is a sphere. The border cases consist of Veronese embeddings of the four projective planes.
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Externí odkaz:
http://arxiv.org/abs/2408.05909
In this paper we study the space $\mathbb{L}(n)$ of $n$-gons in the plane degenerated to segments. We prove that this space is a smooth real submanifold of $\mathbb{C}^n$, and describe its topology in terms of the manifold $\mathbb{M}(n)$ of $n$-gons
Externí odkaz:
http://arxiv.org/abs/2405.13789
Autor:
Freitas, Allan, Guimarães, Felippe
We prove a codimension reduction and congruence theorem for compact $n$-dimensional submanifolds of $\mathbb{S}^{n+p}$ that admit a mean convex isometric embedding into $\mathbb{S}^{n+1}_+$ using a Reilly type formula for space forms.
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Externí odkaz:
http://arxiv.org/abs/2404.12197
Autor:
Iosevich, Alex, Pakianathan, Jonathan
The classical Steinhaus theorem (\cite{Steinhaus1920}) says that if $A \subset {\Bbb R}^d$ has positive Lebesgue measure than $A-A=\{x-y: x,y \in A\}$ contains an open ball. We obtain some quantitative lower bounds on the size of this ball and in som
Externí odkaz:
http://arxiv.org/abs/2401.12112
Autor:
Vrahatis, Michael N.
The Apollonius theorem gives the length of a median of a triangle in terms of the lengths of its sides. The straightforward generalization of this theorem obtained for m-simplices in the n-dimensional Euclidean space for n greater than or equal to m
Externí odkaz:
http://arxiv.org/abs/2401.03232
In this paper, we prove the following version of the famous Bernstein's theorem: Let $X\subset \mathbb R^{n+k}$ be a closed and connected set with Hausdorff dimension $n$. Assume that $X$ satisfies the monotonicity formula at $p\in X$. Then, the foll
Externí odkaz:
http://arxiv.org/abs/2312.01141
In this note, we derive a uniqueness theorem for minimal graphs of general codimension under certain restrictions closed related to the convexity (not strict convexity) of the area functional with respect to singular values, improving the result in \
Externí odkaz:
http://arxiv.org/abs/2311.11075
Classifying the nonflat hypersurfaces in Euclidean space $f\colon M^n\to\mathbb{R}^{n+1}$ that locally admit smooth infinitesimal deformations that preserve the Gauss map infinitesimally was a problem only considered by Schouten \cite{Sc} in 1928. He
Externí odkaz:
http://arxiv.org/abs/2309.16086