• 대한수학회논문집
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• 제14권2호
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• pp.353-364
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• 1999

We found the characterizations for convolution operators in the Beurling`s generalized distribution space to be hyperbolic.

• 대한수학회보
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• 제58권3호
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• pp.721-727
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• 2021

The convex hull of a generic triple of boundary points has non-zero finite volume in complex hyperbolic 2-space.

• 충청수학회지
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• 제28권4호
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• pp.525-535
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• 2015

In this paper, we study on spinors with two hyperbolic components. Firstly, we express the hyperbolic spinor representation of a spacelike curve dened on an oriented (spacelike or time-like) surface in Minkowski space ${\mathbb{R}}^3_1$. Then, we obtain the relation between the hyperbolic spinor representation of the Frenet frame of the spacelike curve on oriented surface and Darboux frame of the surface on the same points. Finally, we give one example about these hyperbolic spinors.

• Korean Journal of Mathematics
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• 제25권2호
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• pp.211-214
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• 2017

In this paper we consider a triple of distinct points in the boundary of quaternionic hyperbolic space and detect where these points are by using the quaternionic triple product.

• 대한수학회지
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• 제40권4호
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• pp.595-607
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• 2003

In the previous paper [6], the author constructed hyperbolic hypersurfaces of degree $2^{n}$ in the n-dimensional complex projective space for every $n\;\geq\;3$. The purpose of this paper is to give some improvement of this result and to show some general methods of constructions of hyperbolic hypersurfaces of higher degree, which enable us to construct hyperbolic hypersurfaces of degree d in the n-dimensional complex projective space for every $d\;\geq\;2\;{\times}\;6^{n}$.

• 대한수학회보
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• 제50권1호
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• pp.97-103
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• 2013

As a suitable application of the well known generalized maximum principle of Omori-Yau, we obtain rigidity results concerning to a complete hypersurface immersed with bounded mean curvature in the $(n+1)$-dimensional hyperbolic space $\mathbb{H}^{n+1}$. In our approach, we explore the existence of a natural duality between $\mathbb{H}^{n+1}$ and the half $\mathcal{H}^{n+1}$ of the de Sitter space $\mathbb{S}_1^{n+1}$, which models the so-called steady state space.

• 대한수학회논문집
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• 제32권4호
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• pp.1009-1024
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• 2017

In this paper, we consider the new faster iterative scheme due to Sintunavarat and Pitea ([32]) for further investigation and we prove its strong and ${\Delta}$-convergence theorems, data dependence and stability results in hyperbolic space. Our results extend, improve and generalize several recent results in CAT(0) space and uniformly convex Banach space.

• 대한수학회논문집
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• 제13권1호
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• pp.171-179
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• 1998

In this paper, we establish Trotted-Kato type convergence theoren for nonlinear semigroups generated by coaccretive operators in a hyperbolic space.

• 대한수학회지
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• 제50권2호
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• pp.425-444
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• 2013

We construct some hyperbolic hyperelliptic space forms whose fundamental groups are generated by only two or three isometries. Each occurring group is obtained from a supergroup, which is an extended Coxeter group generated by plane re ections and half-turns. Then we describe covering properties and determine the isometry groups of the constructed manifolds. Furthermore, we give an explicit construction of space form of the second smallest volume nonorientable hyperbolic 3-manifold with one cusp.

• 대한수학회지
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• 제46권3호
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• pp.513-521
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• 2009

We first introduce a complex hyperbolic space and a complex hyperbolic manifold. After defining the canonical horoball and the canonical cusp on the complex hyperbolic manifold, we estimate the volumes of canonical cusps of complex hyperbolic manifolds. Finally, we deal with cusped, complex hyperbolic 2-manifolds, and in particular, the ones with only one cusp.