2018/04/24 by Derek Jung, Jung, Derek
Mathematics · Physics and Astronomy · #22E25 #26A16 #53C17 #Advanced Differential Geometry Research #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Mathematical Dynamics and Fractals #Metric Geometry (math.MG) #Primary 28A78 #Secondary 58A20
paper · pdf · doi:10.48550/arxiv.1804.09069
openalex publication_date 2018/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose analogues of horizontal and vertical projections for model filiform jet space Carnot groups. Every pair consisting of the jet of a smooth function on ℝ and a vertical hyperplane with first coordinate fixed provides a splitting of a model filiform group, which induces mappings of the group. We prove Marstrand-type theorems for these mappings and determine the possible Hausdorff dimensions of images of sets under these mappings. Analogues of projections for general jet space Carnot groups could be defined similarly.