A characterization of ℓ1 double bubbles with general interface interaction
-
Manuel Friedrich
und
Ulisse Stefanelli
Abstract
We investigate the optimal arrangements of two planar sets of given volume which are minimizing the
Funding source: Deutscher Akademischer Austauschdienst
Award Identifier / Grant number: FR 4083/3-1
Award Identifier / Grant number: EXC 2044-390685587
Funding source: Austrian Science Fund
Award Identifier / Grant number: I4354
Award Identifier / Grant number: 10.55776/ESP88
Award Identifier / Grant number: I4354
Award Identifier / Grant number: F65
Award Identifier / Grant number: I5149
Award Identifier / Grant number: and P 32788
Funding statement: Manuel Friedrich acknowledges support of the DFG project FR 4083/3-1. This work was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC 2044-390685587, Mathematics Münster: Dynamics–Geometry–Structure. Wojciech Górny acknowledges support of the Austrian Science Fund (FWF), grants I4354 and 10.55776/ESP88. Ulisse Stefanelli acknowledges support of the FWF grants I4354, F65, I5149, and P 32788. For the purpose of open access, the authors have applied a CC BY public copyright licence to any Author Accepted Manuscript version arising from this submission.
References
[1] L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems, Oxford Math. Monogr., Oxford University, New York, 2000. 10.1093/oso/9780198502456.001.0001Suche in Google Scholar
[2] W. Boyer, B. Brown, A. Loving and S. Tammen, Double bubbles in hyperbolic surfaces, Involve 11 (2018), no. 2, 207–217. 10.2140/involve.2018.11.207Suche in Google Scholar
[3] M. Carrión Álvarez, J. Corneli, G. Walsh and S. Beheshti, Double bubbles in the three-torus, Exp. Math. 12 (2003), no. 1, 79–89. 10.1080/10586458.2003.10504713Suche in Google Scholar
[4] J. Corneli, I. Corwin, S. Hurder, V. Sesum, Y. Xu, E. Adams, D. Davis, M. Lee, R. Visocchi and N. Hoffman, Double bubbles in Gauss space and spheres, Houston J. Math. 34 (2008), no. 1, 181–204. Suche in Google Scholar
[5]
J. Corneli, N. Hoffman, P. Holt, G. Lee, N. Leger, S. Moseley and E. Schoenfeld,
Double bubbles in
[6] J. Corneli, P. Holt, G. Lee, N. Leger, E. Schoenfeld and B. Steinhurst, The double bubble problem on the flat two-torus, Trans. Amer. Math. Soc. 356 (2004), no. 9, 3769–3820. 10.1090/S0002-9947-04-03551-2Suche in Google Scholar
[7] A. Cotton and D. Freeman, The double bubble problem in spherical space and hyperbolic space, Int. J. Math. Math. Sci. 32 (2002), no. 11, 641–699. 10.1155/S0161171202207188Suche in Google Scholar
[8]
P. Duncan, R. O’Dwyer and E. B. Procaccia,
An elementary proof for the double bubble problem in
[9]
P. Duncan, R. O’Dwyer and E. B. Procaccia,
Discrete
[10]
J. Foisy, M. Alfaro, J. Brock, N. Hodges and J. Zimba,
The standard double soap bubble in
[11] V. Franceschi and G. Stefani, Symmetric double bubbles in the Grushin plane, ESAIM Control Optim. Calc. Var. 25 (2019), Paper No. 77. 10.1051/cocv/2018055Suche in Google Scholar
[12] M. Friedrich, W. Górny and U. Stefanelli, The double-bubble problem on the square lattice, Interfaces Free Bound. 26 (2024), no. 1, 79–134. 10.4171/ifb/510Suche in Google Scholar
[13] M. Hutchings, F. Morgan, M. Ritoré and A. Ros, Proof of the double bubble conjecture, Ann. of Math. (2) 155 (2002), no. 2, 459–489. 10.2307/3062123Suche in Google Scholar
[14] R. Lopez and T. B. Baker, The double bubble problem on the cone, New York J. Math. 12 (2006), 157–167. Suche in Google Scholar
[15] F. Maggi, Sets of Finite Perimeter and Geometric Variational Problems, Cambridge Stud. Adv. Math. 135, Cambridge University, Cambridge, 2012. 10.1017/CBO9781139108133Suche in Google Scholar
[16]
J. D. Masters,
The perimeter-minimizing enclosure of two areas in
[17] E. Milman and J. Neeman, The Gaussian double-bubble and multi-bubble conjectures, Ann. of Math. (2) 195 (2022), no. 1, 89–206. 10.4007/annals.2022.195.1.2Suche in Google Scholar
[18] F. Morgan, Area-minimizing surfaces in cones, Comm. Anal. Geom. 10 (2002), no. 5, 971–983. 10.4310/CAG.2002.v10.n5.a3Suche in Google Scholar
[19]
F. Morgan, C. French and S. Greenleaf,
Wulff clusters in
[20]
B. W. Reichardt,
Proof of the double bubble conjecture in
© 2025 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- A characterization of ℓ1 double bubbles with general interface interaction
- The weak Harnack inequality for unbounded minimizers of elliptic functionals with generalized Orlicz growth
- On the behavior in time of the solutions to total variation flow
- Zaremba problem with degenerate weights
- Point-wise characterizations of limits of planar Sobolev homeomorphisms and their quasi-monotonicity
- Struwe’s global compactness and energy approximation of the critical Sobolev embedding in the Heisenberg group
- On the variational nature of the Anzellotti pairing
- Strongly nonlinear Robin problems for harmonic and polyharmonic functions in the half-space
- Upper semicontinuity of index plus nullity for minimal and CMC hypersurfaces
- A variational approach to the Navier–Stokes equations with shear-dependent viscosity
- Hölder regularity for the fractional p-Laplacian, revisited
- Poincaré inequality and energy of separating sets
- On a class of obstacle problems with (p, q)-growth and explicit u-dependence
- Stepanov differentiability theorem for intrinsic graphs in Heisenberg groups
- Parabolic Lipschitz truncation for multi-phase problems: The degenerate case
Artikel in diesem Heft
- Frontmatter
- A characterization of ℓ1 double bubbles with general interface interaction
- The weak Harnack inequality for unbounded minimizers of elliptic functionals with generalized Orlicz growth
- On the behavior in time of the solutions to total variation flow
- Zaremba problem with degenerate weights
- Point-wise characterizations of limits of planar Sobolev homeomorphisms and their quasi-monotonicity
- Struwe’s global compactness and energy approximation of the critical Sobolev embedding in the Heisenberg group
- On the variational nature of the Anzellotti pairing
- Strongly nonlinear Robin problems for harmonic and polyharmonic functions in the half-space
- Upper semicontinuity of index plus nullity for minimal and CMC hypersurfaces
- A variational approach to the Navier–Stokes equations with shear-dependent viscosity
- Hölder regularity for the fractional p-Laplacian, revisited
- Poincaré inequality and energy of separating sets
- On a class of obstacle problems with (p, q)-growth and explicit u-dependence
- Stepanov differentiability theorem for intrinsic graphs in Heisenberg groups
- Parabolic Lipschitz truncation for multi-phase problems: The degenerate case
