11 papers · 1 filter
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…
Moment-like maps and real algebraic functions with prescribed preimages
Naoki Kitazawa
We discuss a problem on singularity theory of differentiable (smooth) or real algebraic maps which is different from knowing existence and has been difficult: constructing explcit…
Refined algebraic domains with finite sets in the boundaries
Naoki Kitazawa
Refined algebraic domains are regions in the plane surrounded by finitely many non-singular real algebraic curves which may intersect with normal crossing. We are interested in sha…
Arrangements of circles, the regions surrounded by them and labeled Poincaré-Reeb graphs
Naoki Kitazawa
We are interested in arrangements of circles and the regions surrounded by them. {\it Poincaré-Reeb graphs} have been fundamental and strong tools in studying shapes of regions sur…
Realizations of planar graphs as Poincar'e-Reeb graphs of refined algebraic domains
Naoki Kitazawa
Algebraic domains are regions in the plane surrounded by mutually disjoint non-singular real algebraic curves. Poincar'e-Reeb Graphs of them are graphs they naturally collapse: suc…
Arrangements of circles supported by small chords and compatible with natural real algebraic functions
Naoki Kitazawa
We have previously proposed a study of arrangements of small circles which also surround regions in the plane realized as the images of natural real algebraic maps yielding Morse-B…
Arrangements of small circles for Morse-Bott functions
Naoki Kitazawa
As a topic of mathematics, "arrangements", systems of hyperplanes, circles, and general (regular) submanifolds, attract us strongly. We present a natural elementary study of arrang…