Can one hear the dimension of a fractal?

1986/03/01 by Jean Brossard, Ren� Carmona · 3 citations
Computer Science · Mathematics · #Boundary (topology) #Bounded function #Combinatorics #Conjecture #Dimension (graph theory) #Dimension function #Fractal #Fractal dimension #Geometry #Hausdorff dimension #Hausdorff measure #Laplace operator #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Measure (data warehouse) #Minkowski space #Minkowski–Bouligand dimension #Partition (number theory) #Partition function (quantum field theory) #Physics #Pure mathematics #Quantum mechanics #Spectral Theory in Mathematical Physics #Topological and Geometric Data Analysis

paper · doi:10.1007/bf01210795

crossref issued 1986/03/01 · crossref published 1986/03/01 · crossref published-print 1986/03/01 · openalex publication_date 1986/03/01 · crossref created 2005/02/25 · crossref deposited 2019/05/02 · openalex created_date 2025/10/10 · crossref indexed 2026/03/11 · openalex updated_date 2026/07/23

Citations

• Can One Hear the Shape of a Drum?
• Second term of the spectral asymptotic expansion of the Laplace - Beltrami operator on manifolds with boundary

Cited by

• The Riemann Zeta-Function and the One-Dimensional Weyl-Berry Conjecture for Fractal Drums
• Counterexamples to the modified Weyl–Berry conjecture on fractal drums
• Hearing the shape of a drum [wikipedia]