Metric spaces which cannot be isometrically embedded in Hilbert space
1984 ◽
Vol 30
(2)
◽
pp. 161-167
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Let A1A2A3A4, be a planar convex quadrangle with diagonals A1A3 and A2A4. Is there a quadrangle B1B2B3B4 in Euclidean space such that A1A3 < B1B3, A2A4 < B2B4 but AiAj > BiBj for other edges?The answer is “no”. It seems to be obvious but the proof is more difficult. In this paper we shall solve similar more complicated problems by using a higher dimensional geometric inequality which is a generalisation of the well-known Pedoe inequality (Proc. Cambridge Philos. Soc.38 (1942), 397–398) and an interesting result by L.M. Blumenthal and B.E. Gillam (Amer. Math. Monthly50 (1943), 181–185).
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1978 ◽
Vol 1
(4)
◽
pp. 421-431
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The mathematical foundations of anelasticity: existence of smooth global intermediate configurations
2021 ◽
Vol 477
(2245)
◽
pp. 20200462
Keyword(s):
Keyword(s):
2008 ◽
Vol 464
(2094)
◽
pp. 1503-1524
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