Decomposition of integral metric currents

نویسندگان

چکیده

In the setting of complete metric spaces, we prove that integral currents can be decomposed as a sum indecomposable components. special case one-dimensional currents, also show ones are exactly those associated with injective Lipschitz curves or loops, therefore extending Federer's characterisation to spaces. Moreover, some applications our main results will discussed.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Flat Norm Decomposition of Integral Currents

Currents represent generalized surfaces studied in geometric measure theory. They range from relatively tame integral currents representing oriented compact manifolds with boundary and integer multiplicities, to arbitrary elements of the dual space of differential forms. The flat norm provides a natural distance in the space of currents, and works by decomposing a d-dimensional current into dan...

متن کامل

Flat Convergence for Integral Currents in Metric Spaces

It is well known that in compact local Lipschitz neighborhood retracts in Rn flat convergence for Euclidean integer rectifiable currents amounts just to weak convergence. The purpose of the present paper is to extend this result to integral currents in complete metric spaces admitting a local cone type inequality. This includes for example all Banach spaces and complete CAT(κ)-spaces, κ ∈ R. Th...

متن کامل

Currents in Metric Spaces

We develop a theory of currents in metric spaces which extends the classical theory of Federer–Fleming in euclidean spaces and in Riemannian manifolds. The main idea, suggested in [20, 21], is to replace the duality with differential forms with the duality with (k+ 1)-ples (f, π1, . . . , πk) of Lipschitz functions, where k is the dimension of the current. We show, by a metric proof which is ne...

متن کامل

Plateau’s problem for integral currents in locally non-compact metric spaces

The purpose of this article is to prove existence of mass minimizing integral currents with prescribed possibly non-compact boundary in all dual Banach spaces and furthermore in certain spaces without linear structure, such as injective metric spaces and Hadamard spaces. We furthermore prove a weak -compactness theorem for integral currents in dual spaces of separable Banach spaces. Our theorem...

متن کامل

Institute for Mathematical Physics Currents in Metric Spaces Currents in Metric Spaces

We develop a theory of currents in metric spaces which extends the classical theory of Federer{Fleming in euclidean spaces and in Riemannian manifolds. The main idea, suggested in 20, 21], is to replace the duality with diierential forms with the duality with (k + 1)-ples (f; 1; : : : ; k) of Lipschitz functions, where k is the dimension of the current. We show, by a metric proof which is new e...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Journal of Functional Analysis

سال: 2022

ISSN: ['0022-1236', '1096-0783']

DOI: https://doi.org/10.1016/j.jfa.2021.109378