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296:
382:; Maehara, Hiroshi; Pang, Sabrina Xing Mei; Zeng, Zhenbing (2019), "On the Structure of Discrete Metric Spaces Isometric to Circles", in Du, Ding{-}Zhu; Li, Lian; Sun, Xiaoming; Zhang, Jialin (eds.),
275:
198:
121:
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69:, but this term has also been used for other concepts. A metric circle, defined in this way, is unrelated to and should be distinguished from a
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Algorithmic
Aspects in Information and Management – 13th International Conference, AAIM 2019, Beijing, China, August 6–8, 2019, Proceedings
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352:
414:
Katz, Mikhail (1991), "On neighborhoods of the
Kuratowski imbedding beyond the first extremum of the diameter functional",
572:
798:
687:
712:
737:
717:
359:, according to which the unit hemisphere is the minimum-area surface having the Riemannian circle as its boundary.
50:
of bounded length. The metric spaces that can be embedded into metric circles can be characterized by a four-point
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A metric space is a subspace of a metric circle (or of an equivalently defined metric line, interpreted as a
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on the
Riemannian circle. This difference in internal metrics between the hemisphere and the disk led
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347:, for which opposite points on the unit disk would have distance 2, instead of their distance
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case of a metric circle) if every four of its points can be permuted and labeled as
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35:
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17:
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386:, Lecture Notes in Computer Science, vol. 11640, Springer, pp. 83–94,
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39:
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73:, the subset of a metric space within a given radius from a central point.
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484:
those curves on whose developments into the
Euclidean space are circles.
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can be embedded, without any change of distance, into the metric of
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339:. The same metric space would also be obtained from distances on a
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are the same as the distance between the same points on a
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129:
91:
269:
192:
115:
277:. A space with this property has been called a
123:so that they obey the equalities of distances
546:
452:"On certain mappings of Riemannian manifolds"
8:
588:Grothendieck–Hirzebruch–Riemann–Roch theorem
553:
539:
531:
733:Riemann–Roch theorem for smooth manifolds
427:
311:into which the circle divides the sphere.
205:
128:
90:
27:Great circle with a characteristic length
57:Some authors have called metric circles
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343:. This differs from the boundary of a
7:
270:{\displaystyle D(b,c)+D(c,d)=D(b,d)}
193:{\displaystyle D(a,b)+D(b,c)=D(a,c)}
61:, especially in connection with the
698:Riemannian connection on a surface
603:Measurable Riemann mapping theorem
25:
771:
770:
502:Journal of Differential Geometry
683:Riemann's differential equation
593:Hirzebruch–Riemann–Roch theorem
48:rectifiable simple closed curve
708:Riemann–Hilbert correspondence
578:Generalized Riemann hypothesis
498:"Filling Riemannian manifolds"
264:
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1:
743:Riemann–Siegel theta function
331:, by mapping the circle to a
77:Characterization of subspaces
758:Riemann–von Mangoldt formula
456:Nagoya Mathematical Journal
392:10.1007/978-3-030-27195-4_8
830:
753:Riemann–Stieltjes integral
748:Riemann–Silberstein vector
723:Riemann–Liouville integral
288:
766:
688:Riemann's minimal surface
568:
468:10.1017/S0027763000011491
46:, or equivalently on any
713:Riemann–Hilbert problems
618:Riemann curvature tensor
583:Grand Riemann hypothesis
573:Cauchy–Riemann equations
496:Gromov, Mikhael (1983),
429:10.4064/fm-137-3-161-175
638:Riemann mapping theorem
450:Kurita, Minoru (1965),
357:filling area conjecture
291:Filling area conjecture
116:{\displaystyle a,b,c,d}
63:filling area conjecture
738:Riemann–Siegel formula
718:Riemann–Lebesgue lemma
653:Riemann series theorem
514:10.4310/jdg/1214509283
312:
271:
194:
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678:Riemann zeta function
337:great-circle distance
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279:circular metric space
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195:
118:
728:Riemann–Roch theorem
416:Polska Akademia Nauk
380:Dress, Andreas W. M.
204:
127:
89:
799:Riemannian geometry
703:Riemannian geometry
613:Riemann Xi function
598:Local zeta function
299:Arc distances on a
67:Riemannian geometry
623:Riemann hypothesis
482:Riemannian circles
335:and its metric to
313:
267:
190:
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59:Riemannian circles
30:In mathematics, a
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693:Riemannian circle
633:Riemann invariant
401:978-3-030-27194-7
52:triangle equality
18:Riemannian circle
16:(Redirected from
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814:Bernhard Riemann
774:
773:
628:Riemann integral
608:Riemann (crater)
562:Bernhard Riemann
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480:Here we mean by
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809:Metric geometry
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673:Riemann surface
648:Riemann problem
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315:The Riemannian
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663:Riemann sphere
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422:(3): 161–175,
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353:Mikhael Gromov
289:Main article:
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32:metric circle
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643:Riemann form
508:(1): 1–147,
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355:to pose his
333:great circle
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301:great circle
278:
80:
58:
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36:metric space
31:
29:
668:Riemann sum
462:: 121–142,
329:unit sphere
319:of length 2
317:unit circle
309:hemispheres
71:metric ball
793:Categories
363:References
341:hemisphere
83:degenerate
40:arc length
345:unit disk
325:geodesics
777:Category
804:Circles
522:0697984
476:0175062
438:1110030
285:Filling
34:is the
520:
474:
436:
398:
305:sphere
44:circle
327:on a
42:on a
396:ISBN
200:and
510:doi
464:doi
424:doi
420:137
388:doi
65:in
38:of
795::
518:MR
516:,
506:18
504:,
500:,
478:,
472:MR
470:,
460:25
458:,
454:,
434:MR
432:,
418:,
394:,
371:^
281:.
54:.
554:e
547:t
540:v
512::
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349:Ď€
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241:d
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232:(
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220:c
217:,
214:b
211:(
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185:c
182:,
179:a
176:(
173:D
170:=
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164:c
161:,
158:b
155:(
152:D
149:+
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143:b
140:,
137:a
134:(
131:D
111:d
108:,
105:c
102:,
99:b
96:,
93:a
20:)
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