Abstract
In this paper, we use a recent Lipschitz-type condition, called L condition, to state different area formulas in the context of metric measure spaces. We first provide area formulas for mappings between general metric measure spaces and appropriate Euclidean space. That includes area formulas for the graph mapping of a function between a metric measure space and the Euclidean space \(\mathbb {R}^{n}\), and for metric-valued mappings with domain \(\mathbb {R}^{n}\). Finally, and under the assumption of n-rectifiable domains, we provide a general area formula for functions between metric measure spaces.
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Acknowledgements
We would like to thank the referee for his/her very useful comments and suggestions. P. Ochoa has been supported by CONICET. M. Garriga and P. Ochoa have been partially supported by Grant B017-T1, UNCUYO, Argentina.
Funding
P. Ochoa has been supported by CONICET. M. Garriga and P. Ochoa have been partially supported by Grant B017-T1, UNCUYO, Argentina.
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Garriga, M., Ochoa, P. Area Formulas in Metric Measure Spaces Under a Weak Lipschitz-Like Condition. Results Math 78, 38 (2023). https://doi.org/10.1007/s00025-022-01807-0
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DOI: https://doi.org/10.1007/s00025-022-01807-0