Gel'fand's inverse problem under Ricci curvature bounds
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914331709407232 |
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| author | Honda, Shouhei Lu, Jinpeng |
| author_facet | Honda, Shouhei Lu, Jinpeng |
| contents | The classical Gel'fand's inverse problem asks whether a Riemannian manifold is uniquely determined by the knowledge of the heat kernel on any open subset of the manifold. We study this inverse problem in the non-smooth setting in the framework of ${\rm RCD}(K,N)$ spaces, namely, metric-measure spaces with synthetic Riemannian Ricci curvature bounded below by $K$ and dimension bounded above by $N$. We establish the unique solvability of Gel'fand's inverse problem for the class of compact ${\rm RCD}(K,N)$ spaces whose regular set admits $C^1$-Riemannian structure. As an application, we obtain the stability of Gel'fand's inverse problem in the class of closed Riemannian manifolds with bounded Ricci curvature, diameter and volume bounded from below. We note that the results are new even for Einstein orbifolds and (weighted) Riemannian manifolds with non-smooth boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14527 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Gel'fand's inverse problem under Ricci curvature bounds Honda, Shouhei Lu, Jinpeng Differential Geometry Analysis of PDEs Metric Geometry 35R30, 53C23, 58J50 The classical Gel'fand's inverse problem asks whether a Riemannian manifold is uniquely determined by the knowledge of the heat kernel on any open subset of the manifold. We study this inverse problem in the non-smooth setting in the framework of ${\rm RCD}(K,N)$ spaces, namely, metric-measure spaces with synthetic Riemannian Ricci curvature bounded below by $K$ and dimension bounded above by $N$. We establish the unique solvability of Gel'fand's inverse problem for the class of compact ${\rm RCD}(K,N)$ spaces whose regular set admits $C^1$-Riemannian structure. As an application, we obtain the stability of Gel'fand's inverse problem in the class of closed Riemannian manifolds with bounded Ricci curvature, diameter and volume bounded from below. We note that the results are new even for Einstein orbifolds and (weighted) Riemannian manifolds with non-smooth boundary. |
| title | Gel'fand's inverse problem under Ricci curvature bounds |
| topic | Differential Geometry Analysis of PDEs Metric Geometry 35R30, 53C23, 58J50 |
| url | https://arxiv.org/abs/2602.14527 |