Steklov-isospectral Euclidean domains

Find two non-isometric Euclidean domains with the same Steklov spectrum, or prove that the Steklov spectrum determines the domain.

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1	{
2	"domain": "mathematics",
3	"topics": [
4	"analysis",
5	"geometry-topology"
6	],
7	"type": "construction",
8	"also": [
9	"proof"
10	],
11	"source": {
12	"key": "aimpl",
13	"name": "AIM Problem Lists",
14	"url": "http://aimpl.org/stekloveigen/5/",
15	"id": "stekloveigen 5.2",
16	"curator": "American Institute of Mathematics",
17	"poser": "Leonid Parnovski",
18	"status": "open",
19	"as_of": "2026-10-20",
20	"catalog": "0521c19bbd38"
21	},
22	"review": true,
23	"approval": "first-time"
24	}