| Change of variables formula for Borel functions | statement | proposition 6.1 | arxiv |
| Alexandrov maximum principle | statement | proposition 3.12 | arxiv |
| Cylindrical-data uniqueness | statement | theorem 1.2 | arxiv |
| Hausdorff measure | example | example 2.2 | arxiv |
| Convergence of subgradients | statement | lemma 2.13 | arxiv |
| Extremal boundary slope | statement | proposition 4.2 | arxiv |
| Alexandrov solution | definition | definition 3.6 | arxiv |
| Integral identity for equal Cauchy pairs | statement | corollary 6.3 | arxiv |
| Subdifferential | definition | definition 2.7 | arxiv |
| Subdifferential images | definition | definition 5.1 | arxiv |
| Singular Monge--Ampère measures | example | example 3.5 | arxiv |
| 6ZA1RWRXRM | definition | definition 1.1 | arxiv |
| Monge--Ampère measure | statement | lemma 3.3 | arxiv |
| Boundary slope as interior normal derivative | statement | lemma 4.11 | arxiv |
| Dirichlet-to-interior-Neumann map | statement | proposition 4.13 | arxiv |
| Boundary Lipschitz bound | statement | proposition 4.12 | arxiv |
| Legendre transform | definition | definition 5.5 | arxiv |
| Well-posedness of the Dirichlet problem | statement | proposition 3.14 | arxiv |
| Compactness of subgradients | statement | lemma 2.12 | arxiv |
| Dirichlet-to-interior-Neumann formulation | statement | corollary 1.4 | arxiv |
| Scaling, translation invariance, superadditivity, and monotonicity | statement | proposition 3.9 | arxiv |
| Compatibility with classical Cauchy data | statement | proposition 4.8 | arxiv |
| CTMC0107WR | statement | lemma 2.3 | arxiv |
| Classical Cauchy data | definition | definition 4.7 | arxiv |
| Cylindrical-data uniqueness for gradient weights | statement | theorem 1.5 | arxiv |
| Defining function formulation | statement | lemma 2.15 | arxiv |
| EK8TG0ZH94 | statement | lemma 5.3 | arxiv |
| Supporting hyperplanes and strict convexity | statement | corollary 2.5 | arxiv |
| Weak continuity property | statement | proposition 3.11 | arxiv |
| Interior Cauchy data | definition | definition 4.9 | arxiv |
| Properties of Legendre transform | statement | proposition 5.6 | arxiv |
| Global uniqueness | statement | corollary 1.3 | arxiv |
| MNA25TR9QZ | definition | definition 2.14 | arxiv |
| Degenerate limit | statement | lemma 7.1 | arxiv |
| Unique subgradients | statement | lemma 2.10 | arxiv |
| Differentiability of convex functions | statement | lemma 2.9 | arxiv |
| Measurability | statement | lemma 4.4 | arxiv |
| Almost-everywhere second-order boundary geometry | statement | lemma A.1 | arxiv |
| R3RQ61HW7A | statement | lemma 3.1 | arxiv |
| Equality of subdifferential images | statement | corollary 5.8 | arxiv |
| Boundary subdifferential | statement | lemma 4.1 | arxiv |
| Weak convergence of locally finite Borel measures | statement | proposition 3.10 | arxiv |
| Boundary subdifferential ray | statement | lemma 4.3 | arxiv |
| Nullity of the boundary slope image | statement | lemma 5.4 | arxiv |
| Comparison principle | statement | proposition 3.13 | arxiv |
| Boundary characterization of $\mathrm D_u$ | statement | proposition 5.7 | arxiv |
| Generalized Cauchy data set for $L^1$ sources | definition | definition 4.6 | arxiv |
| YKFN0Z3VRC | definition | definition 3.2 | arxiv |
| Strictly convex domains | definition | definition 2.4 | arxiv |
| Generalized global Cauchy data | statement | proposition 4.5 | arxiv |
