R. Komendarczyk

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math.AT2026

Vietoris--Rips Shadow for Euclidean Graph Reconstruction

Rafal Komendarczyk, Sushovan Majhi, Atish Mitra

The shadow of an abstract simplicial complex $K$ with vertices in $R^{N}$ is a subset of $R^{N}$ defined as the union of the convex hulls of simplices of $K$ . The Vie…

math.AT2026

Topological Stability and Latschev-type Reconstruction Theorems for Spaces of Curvature Bounded Above

Rafal Komendarczyk, Sushovan Majhi, Will Tran

We consider the problem of homotopy-type reconstruction of compact subsets $X \subset R^{N}$ that have the Alexandrov curvature bounded above ( $\leq$ $I^º$ ) in the intrinsic length met…