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Volumn 44, Issue 3-4, 2012, Pages 477-494

Local Poincaré inequalities from stable curvature conditions on metric spaces

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EID: 84860626444     PISSN: 09442669     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00526-011-0442-7     Document Type: Article
Times cited : (182)

References (23)
  • 3
    • 0000720752 scopus 로고
    • A note on the isoperimetric constant
    • Buser P.: A note on the isoperimetric constant. Ann. Sci. cole Norm. Sup. 15, 213-230 (1982).
    • (1982) Ann. Sci. Cole Norm. Sup. , vol.15 , pp. 213-230
    • Buser, P.1
  • 4
    • 0033456306 scopus 로고    scopus 로고
    • Differentiability of Lipschitz functions on metric measure spaces
    • Cheeger J.: Differentiability of Lipschitz functions on metric measure spaces. Geom. Funct. Anal. 9, 428-517 (1999).
    • (1999) Geom. Funct. Anal. , vol.9 , pp. 428-517
    • Cheeger, J.1
  • 5
    • 0002157976 scopus 로고    scopus 로고
    • On the structure of spaces with Ricci curvature bounded below. III
    • Cheeger J., Colding T.: On the structure of spaces with Ricci curvature bounded below. III. J. Differential Geom. 54, 37-74 (2000).
    • (2000) J. Differential Geom. , vol.54 , pp. 37-74
    • Cheeger, J.1    Colding, T.2
  • 6
    • 54349129004 scopus 로고    scopus 로고
    • Eulerian calculus for the displacement convexity in the Wasserstein distance
    • Daneri S., Savaré G.: Eulerian calculus for the displacement convexity in the Wasserstein distance. SIAM J. Math. Anal. 40, 1104-1122 (2008).
    • (2008) SIAM J. Math. Anal. , vol.40 , pp. 1104-1122
    • Daneri, S.1    Savaré, G.2
  • 7
    • 34547435369 scopus 로고    scopus 로고
    • Strong displacement convexity on Riemannian manifolds
    • Figalli A., Villani C.: Strong displacement convexity on Riemannian manifolds. Math. Z. 257, 251-259 (2007).
    • (2007) Math. Z. , vol.257 , pp. 251-259
    • Figalli, A.1    Villani, C.2
  • 12
    • 0002048617 scopus 로고    scopus 로고
    • Quasiconformal maps in metric spaces with controlled geometry
    • Heinonen J., Koskela P.: Quasiconformal maps in metric spaces with controlled geometry. Acta Math. 181, 1-61 (1998).
    • (1998) Acta Math. , vol.181 , pp. 1-61
    • Heinonen, J.1    Koskela, P.2
  • 13
    • 62049083002 scopus 로고    scopus 로고
    • Ricci curvature for metric-measure spaces via optimal transport
    • Lott J., Villani C.: Ricci curvature for metric-measure spaces via optimal transport. Ann. Math. 169, 903-991 (2009).
    • (2009) Ann. Math. , vol.169 , pp. 903-991
    • Lott, J.1    Villani, C.2
  • 14
    • 33847377614 scopus 로고    scopus 로고
    • Weak curvature conditions and functional inequalities
    • Lott J., Villani C.: Weak curvature conditions and functional inequalities. J. Funct. Anal. 245, 311-333 (2007).
    • (2007) J. Funct. Anal. , vol.245 , pp. 311-333
    • Lott, J.1    Villani, C.2
  • 15
    • 0031161793 scopus 로고    scopus 로고
    • A convexity principle for interacting gases
    • McCann R. J.: A convexity principle for interacting gases. Adv. Math. 128, 153-179 (1997).
    • (1997) Adv. Math. , vol.128 , pp. 153-179
    • McCann, R.J.1
  • 16
    • 68149156285 scopus 로고    scopus 로고
    • Gradient flows on Wasserstein spaces over compact Alexandrov spaces
    • Ohta S.-i.: Gradient flows on Wasserstein spaces over compact Alexandrov spaces. Am. J. Math. 131, 475-516 (2009).
    • (2009) Am. J. Math. , vol.131 , pp. 475-516
    • Ohta, S.-I.1
  • 17
    • 35649015387 scopus 로고    scopus 로고
    • On the measure contraction property of metric measure spaces
    • Ohta S.-i.: On the measure contraction property of metric measure spaces. Comment. Math. Helv. 82, 805-828 (2007).
    • (2007) Comment. Math. Helv. , vol.82 , pp. 805-828
    • Ohta, S.-I.1
  • 18
    • 39349107061 scopus 로고    scopus 로고
    • On local Poincaré via transportation
    • von Renesse M.-K.: On local Poincaré via transportation. Math. Z. 259, 21-31 (2008).
    • (2008) Math. Z. , vol.259 , pp. 21-31
    • von Renesse, M.-K.1
  • 19
    • 34547422503 scopus 로고    scopus 로고
    • Gradient flows and diffusion semigroups in metric spaces under lower curvature bounds
    • Savaré G.: Gradient flows and diffusion semigroups in metric spaces under lower curvature bounds. C. R. Math. Acad. Sci. Paris 345, 151-154 (2007).
    • (2007) C. R. Math. Acad. Sci. Paris , vol.345 , pp. 151-154
    • Savaré, G.1
  • 20
    • 0001010413 scopus 로고    scopus 로고
    • Finding curves on general spaces through quantitative topology, with applications to Sobolev and Poincaré inequalities
    • Semmes S.: Finding curves on general spaces through quantitative topology, with applications to Sobolev and Poincaré inequalities. Selecta Math. 2, 155-295 (1996).
    • (1996) Selecta Math. , vol.2 , pp. 155-295
    • Semmes, S.1
  • 21
    • 33750180350 scopus 로고    scopus 로고
    • On the geometry of metric measure spaces. I
    • Sturm K.-T.: On the geometry of metric measure spaces. I. Acta Math. 196, 65-131 (2006).
    • (2006) Acta Math. , vol.196 , pp. 65-131
    • Sturm, K.-T.1
  • 22
    • 33750180350 scopus 로고    scopus 로고
    • On the geometry of metric measure spaces. II
    • Sturm K.-T.: On the geometry of metric measure spaces. II. Acta Math. 196, 133-177 (2006).
    • (2006) Acta Math. , vol.196 , pp. 133-177
    • Sturm, K.-T.1
  • 23
    • 37349070894 scopus 로고    scopus 로고
    • Grundlehren Der Mathematischen Wissenschaften Berlin: Springer-Verlag
    • Villani C.: Optimal transport. Old and new, vol. 338 of Grundlehren der Mathematischen Wissenschaften. Springer-Verlag, Berlin (2009).
    • (2009) Optimal Transport. Old and New , vol.338
    • Villani, C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.