13 papers
Reeb spaces of functions being analytic on dense subsets and their graph structures
Naoki Kitazawa
Reeb spaces of real-valued functions on manifolds are the spaces of all connected components (contours) of level sets and endowed with the natural quotient topology. They have been…
Regions surrounded by cylinders of circles of fixed radii and exposition of their shapes by natural graphs
Naoki Kitazawa
We investigate regions formed by cylinders of circles of fixed radii. We investigate graphs obtained by collapsing each level set of the functions represented by the natural projec…
Regions surrounded by circles whose Poincaré-Reeb graphs are trees
Naoki Kitazawa
Regions in the Euclidean plane surrounded by circles are fundamental geometric and combinatorial objects. Related studies have been done and we cannot explain them precisely, or ro…
Planar graphs embedded in generic ways and realizing them as Reeb graphs of real algebraic functions
Naoki Kitazawa
This paper is concerned with long-time interest of us, especially, the author, in realizing graphs as Reeb graphs of real algebraic functions of certain nice classes. The Reeb grap…
Graphs with tree decompositions of small graphs and realizing them as the Reeb graphs of real algebraic functions
Naoki Kitazawa
We have been interested in graphs and realizing them as Reeb graphs of explicit real algebraic functions. The Reeb graph of a differentiable function is the quotient space of the m…
Reconstruction of real algebraic functions into curves with prescribed Reeb graphs
Naoki Kitazawa
We discuss reconstructing smooth real algebraic maps onto curves whose Reeb graph is as prescribed. This can be contributed to real algebraic geometry, especially in explicit examp…