2 papers
math.DG2026
Envelopes created by curve families in the Lorentz-Minkowski plane
Masatomo Takahashi, Yongqiao Wang
Classical definitions of envelopes are vague for singular curves in the Lorentz-Minkowski plane. To study envelopes of such curves, we introduce a family of smooth curves that may…
math.DG2026
Envelopes created by sphere families in Euclidean 3-space
Takashi Nishimura, Masatomo Takahashi, Yongqiao Wang
In this paper, on envelopes created by sphere families in Euclidean 3-space, all four basic problems (existence problem, representation problem, problem on the number of envelopes,…