Lipschitz Algebras and Derivations II. Exterior Differentiation

Weaver, Nik

doi:10.1006/jfan.2000.3637

Cited by 78 publications

(107 citation statements)

References 48 publications

Supporting

Mentioning

104

Contrasting

Order By: Relevance

“…Various interactions with other areas have emerged and should be further explored. In this context we just mention the functions of bounded higher variation [8,9,21,24,27], the recent progress on (generalized) flat chains [1,18,36,37], the scans from [10,11,16], the differentiation theory on metric measure spaces [4,5,22], and the derivations from [29,30]. We refer to [19] for an excellent survey of some of these and further related topics.…”

Section: Introductionmentioning

confidence: 98%

Local Currents in Metric Spaces

Lang

2010

J Geom Anal

189

View full text Add to dashboard Cite

Ambrosio and Kirchheim presented a theory of currents with finite mass in complete metric spaces. We develop a variant of the theory that does not rely on a finite mass condition, closely paralleling the classical Federer-Fleming theory. If the underlying metric space is an open subset of a Euclidean space, we obtain a natural chain monomorphism from general metric currents to general classical currents whose image contains the locally flat chains and which restricts to an isomorphism for locally normal currents. We give a detailed exposition of the slicing theory for locally normal currents with respect to locally Lipschitz maps, including the rectifiable slices theorem, and of the compactness theorem for locally integral currents in locally compact metric spaces, assuming only standard results from analysis and measure theory.

show abstract

Section: Introductionmentioning

confidence: 98%

Local Currents in Metric Spaces

Lang

2010

J Geom Anal

189

View full text Add to dashboard Cite

show abstract

“…This section essentially comes from [14,15,16]. The notion of measurable metric was first formulated in [12].…”

Section: Measurable Metrics and Lipschitz Functionsmentioning

confidence: 99%

“…]) and in the book [14]. Moreover, in [15] an exterior differential calculus was constructed in this general setting.…”

Section: Introductionmentioning

confidence: 99%

“…In [15], N. Weaver studied, in the framework of Dirichlet structures satisfying the hypotheses of locality and of existence of a carré du champ operator (in the sense of [1]), the relationship between intrinsic metric and measurable metric. One of the aims of the present paper (see Section 3) is to come back to this study with essentially the same basic ideas, but in bringing some modifications and complements which seem useful.…”

Section: Introductionmentioning

confidence: 99%

“…To this respect, we bring some precisions and complements to [15], notably concerning links with the notion of intrinsic metric ([2]). In the particular case of an abstract Wiener space, we establish the relationship between these notions and that of H -metric ([5]) and µ-a.e.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Intrinsic metrics and Lipschitz functions

Hirsch¹

2003

Journal of Evolution Equations

View full text Add to dashboard Cite

We study the notions of measurable metric and Lipschitz function which were introduced by N. Weaver ([12]), in the framework of Dirichlet spaces. To this respect, we bring some precisions and complements to [15], notably concerning links with the notion of intrinsic metric ([2]). In the particular case of an abstract Wiener space, we establish the relationship between these notions and that of H -metric ([5]) and µ-a.e. H -Lipschitz continuous function ([4]).francis hirsch J.evol.equ.francis hirsch J.evol.equ.

show abstract

Constancy of the Dimension for RCD(K,N) Spaces via Regularity of Lagrangian Flows

Bruè

Semola

2019

Comm Pure Appl Math

View full text Add to dashboard Cite

We prove a regularity result for Lagrangian flows of Sobolev vector fields over RCD(K, N ) metric measure spaces, regularity is understood with respect to a newly defined quasi-metric built from the Green function of the Laplacian. Its main application is that RCD(K, N ) spaces have constant dimension. In this way we generalize to such abstract framework a result proved by Colding-Naber for Ricci limit spaces, introducing ingredients that are new even in the smooth setting. * Scuola Normale Superiore, elia.brue@sns.it. † Scuola Normale Superiore, daniele.semola@sns.it.

show abstract

Lipschitz Algebras and Derivations II. Exterior Differentiation

Cited by 78 publications

References 48 publications

Local Currents in Metric Spaces

Local Currents in Metric Spaces

Intrinsic metrics and Lipschitz functions

Constancy of the Dimension for RCD(K,N) Spaces via Regularity of Lagrangian Flows

Contact Info

Product

Resources

About