real analyticity
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2020 ◽  
Vol 29 (07) ◽  
pp. 2050047
Author(s):  
Atsufumi Honda ◽  
Kosuke Naokawa ◽  
Kentaro Saji ◽  
Masaaki Umehara ◽  
Kotaro Yamada

Letting [Formula: see text] be a compact [Formula: see text]-curve embedded in the Euclidean [Formula: see text]-space ([Formula: see text] means real analyticity), we consider a [Formula: see text]-cuspidal edge [Formula: see text] along [Formula: see text]. When [Formula: see text] is non-closed, in the authors’ previous works, the local existence of three distinct cuspidal edges along [Formula: see text] whose first fundamental forms coincide with that of [Formula: see text] was shown, under a certain reasonable assumption on [Formula: see text]. In this paper, if [Formula: see text] is closed, that is, [Formula: see text] is a knot, we show that there exist infinitely many cuspidal edges along [Formula: see text] having the same first fundamental form as that of [Formula: see text] such that their images are non-congruent to each other, in general.


2020 ◽  
Vol 133 ◽  
pp. 167-171 ◽  
Author(s):  
Jacek Bochnak ◽  
János Kollár ◽  
Wojciech Kucharz
Keyword(s):  

2019 ◽  
Vol 147 (12) ◽  
pp. 5251-5256
Author(s):  
Alexander Isaev ◽  
Joël Merker
Keyword(s):  
The Real ◽  

2018 ◽  
Vol 19 (4) ◽  
pp. 1185-1209
Author(s):  
G. Hoepfner ◽  
R. Medrado

We investigate interesting connections between Mizohata type vector fields and microlocal regularity of nonlinear first-order PDEs, establishing results in Denjoy–Carleman classes and real analyticity results in the linear case.


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