15 citations · 23 across the 19 of their papers we have counts for
19 papers
A transversality theorem for multiple-point crossings under generic linear perturbations with Hausdorff measure estimates
Shunsuke Ichiki
We establish a transversality theorem for multiple-point crossings under generic linear perturbations with explicit Hausdorff measure estimates for the exceptional parameter set, a…
Non-density of -stable mappings on non-compact manifolds
Shunsuke Ichiki
The problem of density of -stable mappings is a classical and venerable subject in singularity theory. In 1973, Mather showed that the set of proper -stable mappings is d…
Non-density of stable mappings on non-compact manifolds
Shunsuke Ichiki
Around 1970, Mather established a significant theory on the stability of mappings and gave a characterization of the density of proper stable mappings in the set of all…
All unconstrained strongly convex problems are weakly simplicial
Yusuke Mizota, Naoki Hamada, Shunsuke Ichiki
A multi-objective optimization problem is weakly simplicial if there exists a surjection from a simplex onto the Pareto set/front such that the image of each subsimplex…
A refined transversality theorem on linear perturbations and its applications
Shunsuke Ichiki
In this paper, we establish a refined transversality theorem on linear perturbations from a new perspective of Hausdorff measures. Furthermore, we give its applications not only to…
Simpliciality of strongly convex problems
Naoki Hamada, Shunsuke Ichiki
A multiobjective optimization problem is simplicial if the Pareto set and the Pareto front are diffeomorphic to a simplex and, under the diffeomorphisms, each fac…
Characterization of the equality of weak efficiency and efficiency on convex free disposal hulls
Naoki Hamada, Shunsuke Ichiki
In solving a multi-objective optimization problem by scalarization techniques, solutions to a scalarized problem are, in general, weakly efficient rather than efficient to the orig…
Topology of Pareto sets of strongly convex problems
Naoki Hamada, Kenta Hayano, Shunsuke Ichiki +2
A multiobjective optimization problem is simplicial if the Pareto set and front are homeomorphic to a simplex and, under the homeomorphisms, each face of the simplex corresponds to…
Transversality theorems on generic linearly perturbed mappings
Shunsuke Ichiki
In his celebrated paper "Generic projections", John Mather has given a striking transversality theorem and its applications on generic projections. On the other hand, in this paper…
Characterization of generic transversality
Shunsuke Ichiki
In this paper, the notion of generic transversality and its characterization are given. The characterization is also a further improvement of the basic transversality result and it…
Generic distance-squared mappings on plane curves
Shunsuke Ichiki
A distance-squared function is one of the most significant functions in the application of singularity theory to differential geometry. Moreover, distance-squared mappings are natu…
Geometric interpretation of generalized distance-squared mappings of into
Shunsuke Ichiki
Generalized distance-squared mappings are quadratic mappings of into of special type. In the case that matrices constructed by coefficients of…
Composing generic linearly perturbed mappings and immersions/injections
Shunsuke Ichiki
Let (resp., ) be a manifold (resp., an open subset of ). Let and be an immersion and a mapping, respectively.…
Preservation of immersed or injective properties by composing generic generalized distance-squared mappings
Shunsuke Ichiki, Takashi Nishimura
Any generalized distance-squared mapping of equidimensional case has singularities, and their singularity types are wrapped into mystery in higher dimensional cases. Any generalize…
Generic linear perturbations
Shunsuke Ichiki
In his celebrated paper "Generic projections", John Mather has shown that almost all linear projections from a submanifold of a vector space into a subspace are transverse with res…
Around distance-squared mappings
Shunsuke Ichiki, Takashi Nishimura
This is a survey article on distance-squared mappings and related topics.
Generalized distance-squared mappings of into
S. Ichiki, T. Nishimura
We classify generalized distance-squared mappings of into () having generic central points. Moreover, we show that there does not exi…
Recognizable classification of Lorentzian distance-squared mappings
Shunsuke Ichiki, Takashi Nishimura
The Lorentzian length, which is one of the most significant functions in Lorentzian geometry, is a complex-valued function. Its square gives a real-valued non-degenerate quadratic…
Distance-squared mappings
Shunsuke Ichiki, Takashi Nishimura
A distance-squared function is one of the most significant functions in the application of singularity theory to differential geometry. In this paper, we define naturally extended…