The paper establishes non-trivial dimensional thresholds for volume vectors determined by hypergraphs of simplices via a Jacobian method leveraging distance results and a refinement for planar triangles, improving prior bounds.
Multiparameter projection theorems with applications to sums-products and finite point configurations in the Euclidean set- ting
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On volume vectors determined by hypergraphs in thin subsets of Euclidean space
The paper establishes non-trivial dimensional thresholds for volume vectors determined by hypergraphs of simplices via a Jacobian method leveraging distance results and a refinement for planar triangles, improving prior bounds.