Zobrazeno 1 - 10
of 90
pro vyhledávání: '"58K30"'
Autor:
Reintjes, Moritz, Temple, Blake
We introduce a natural, mathematically consistent definition of the essential (highest possible) regularity of an affine connection -- a geometric property independent of atlas -- together with a checkable necessary and sufficient condition for deter
Externí odkaz:
http://arxiv.org/abs/2412.08928
Autor:
Smith, Graham
We describe the structure of the singular sets of constant curvature, convex hypersurfaces in hyperbolic space for general convex curvature functions. We apply this result to the study of the ideal Plateau problem in hyperbolic space for such curvatu
Externí odkaz:
http://arxiv.org/abs/2410.09950
Autor:
Saeki, Osamu
We study how to construct explicit deformations of generic smooth maps from closed $n$--dimensional manifolds $M$ with $n \geq 4$ to the $2$--sphere $S^2$ and show that every smooth map $M \to S^2$ is homotopic to a $C^\infty$ stable map with at most
Externí odkaz:
http://arxiv.org/abs/2407.10145
We show that two bi-Lipschitz equivalent Brieskorn-Pham hypersurfaces have the same multiplicities at $0$. Moreover we show that if two algebraic $(n-1)$-dimensional cones $P, R\subset\mathbb C^n$ with isolated singularities are homeomorphic, then th
Externí odkaz:
http://arxiv.org/abs/2404.06922
Autor:
Saeki, Osamu, Sakurai, Shuntaro
We consider links of complex isolated hypersurface singularities in $\mathbb{C}^{n+1}$ and study differentiable maps defined by restricting holomorphic functions to the links. We give an explicit example in which such a restriction gives a fold map i
Externí odkaz:
http://arxiv.org/abs/2402.02365
Fr\'echet means of samples from a probability measure $\mu$ on any smoothly stratified metric space M with curvature bounded above are shown to satisfy a central limit theorem (CLT). The methods and results proceed by introducing and proving analytic
Externí odkaz:
http://arxiv.org/abs/2311.09455
Variation of empirical Fr\'echet means on a metric space with curvature bounded above is encoded via random fields indexed by unit tangent vectors. A central limit theorem shows these random tangent fields converge to a Gaussian such field and lays t
Externí odkaz:
http://arxiv.org/abs/2311.09454
Any measure $\mu$ on a CAT(k) space M that is stratified as a finite union of manifolds and has local exponential maps near the Fr\'echet mean $\bar\mu$ yields a continuous "tangential collapse" from the tangent cone of M at $\bar\mu$ to a vector spa
Externí odkaz:
http://arxiv.org/abs/2311.09453
In any CAT(k) space M, the "shadow" of a tangent vector Z at a point p is the set vectors that form an angle of \pi or more with Z. Taking logarithm maps at points approaching p along a fixed geodesic ray from p with tangent Z collapses the shadow to
Externí odkaz:
http://arxiv.org/abs/2311.09451
We show that for every $k\ge 3$ there exist complex algebraic cones of dimension $k$ with isolated singularities, which are bi-Lipschitz and semi-algebraically equivalent but they have different degrees. We also prove that homeomorphic projective hyp
Externí odkaz:
http://arxiv.org/abs/2309.07078