. We will summarize a part of the result of [10], the construction of Sobolev spaces and energy functionals over maps between metric spaces under the strong measure contraction property of Bishop-Gromov type, which is a generalized notion of Ricci curvature bounded below. We also present the notion of generalized measure contraction property, which gives a characterization of energies by approximating energies of Sturm type over Lipschitz maps. Keywords: Dirichlet form, Sobolev space, measure contraction property, subpartitional lemma, \Gamma-limit, Riemannian manifold, Alexandrov space, harmonic map, Bishop inequality, Bishop-Gromov inequality. Mathematics Subject Classifications (1991): Primary: 31C25; Secondary: 53C20, 53C21, 53C22. 1....
We prove that if ( X, d, m) is an essentially non-branching metric measure space with m(X)=1, havin...
We prove the Sobolev-to-Lipschitz property for metric measure spaces satisfying the quasi curvature-...
We prove that if M is a closed n-dimensional Riemannian manifold, n \ge 3, with \mathrm{Ric}\ge n-1 ...
. We construct the (1; p)-Sobolev spaces and energy functionals over L p -maps between metric spac...
We introduce a measure contraction property of metric measure spaces which can be regarded as a gene...
The aim of the present paper is to bridge the gap between the Bakry-Émery and the Lott-Sturm-Villani...
To the memory of Enrico Magenes, whose exemplar life, research and teaching shaped generations of ma...
(v2) Minor typos, proof of Proposition 2.3, proof of Theorem 4.8: corrected. Proof of Theorem 6.2: c...
The aim of the present paper is to bridge the gap between the Bakry-Emery and the Lott-Sturm-Villani...
For metric measure spaces satisfying the reduced curvature-dimension condition CD*(K,N) we prove a s...
We provide a quick overview of various calculus tools and of the main results concerning the heat fl...
The intent of this short note is to extend real valued Lipschitz functions on metric spaces, while l...
We prove that for non-branching metric measure spaces the local curvature condition CD loc(K, N) imp...
Minor typos corrected and many small improvements added. Lemma 2.4, Lemma 2.10, Prop. 5.7, Rem. 5.8,...
A theory of generalized harmonic maps between metric spaces is developed. The energy integral for ma...
We prove that if ( X, d, m) is an essentially non-branching metric measure space with m(X)=1, havin...
We prove the Sobolev-to-Lipschitz property for metric measure spaces satisfying the quasi curvature-...
We prove that if M is a closed n-dimensional Riemannian manifold, n \ge 3, with \mathrm{Ric}\ge n-1 ...
. We construct the (1; p)-Sobolev spaces and energy functionals over L p -maps between metric spac...
We introduce a measure contraction property of metric measure spaces which can be regarded as a gene...
The aim of the present paper is to bridge the gap between the Bakry-Émery and the Lott-Sturm-Villani...
To the memory of Enrico Magenes, whose exemplar life, research and teaching shaped generations of ma...
(v2) Minor typos, proof of Proposition 2.3, proof of Theorem 4.8: corrected. Proof of Theorem 6.2: c...
The aim of the present paper is to bridge the gap between the Bakry-Emery and the Lott-Sturm-Villani...
For metric measure spaces satisfying the reduced curvature-dimension condition CD*(K,N) we prove a s...
We provide a quick overview of various calculus tools and of the main results concerning the heat fl...
The intent of this short note is to extend real valued Lipschitz functions on metric spaces, while l...
We prove that for non-branching metric measure spaces the local curvature condition CD loc(K, N) imp...
Minor typos corrected and many small improvements added. Lemma 2.4, Lemma 2.10, Prop. 5.7, Rem. 5.8,...
A theory of generalized harmonic maps between metric spaces is developed. The energy integral for ma...
We prove that if ( X, d, m) is an essentially non-branching metric measure space with m(X)=1, havin...
We prove the Sobolev-to-Lipschitz property for metric measure spaces satisfying the quasi curvature-...
We prove that if M is a closed n-dimensional Riemannian manifold, n \ge 3, with \mathrm{Ric}\ge n-1 ...