Publications

Recorded here is a list of publications, current through 11/2021.

Journal Articles

  1. Preprint Anthony Gruber. Planar Immersions with Prescribed Curl and Jacobian Determinant are Unique. Bull. Aust. Math. Soc. 1-6 (2021).
    DOI: https://doi.org/10.1017/S0004972721000812.

  2. Preprint Anthony Gruber, Max Gunzburger, Lili Ju, Yuankai Teng, Zhu Wang. Nonlinear Level Set Learning for Function Approximation on Sparse Data with Applications to Parametric Differential Equations. Numer. Math. Theory Methods Appl. (2021). DOI: https://doi.org/10.4208/nmtma.OA-2021-0062.

  3. Preprint Anthony Gruber, Álvaro Pámpano, Magdalena Toda. Regarding the Euler-Plateau Problem with Elastic Modulus. Ann. Mat. Pura. Appl. (2021).
    DOI: https://doi.org/10.1007/s10231-021-01079-5.

  4. Here Anthony Gruber, Eugenio Aulisa. Computational p-Willmore Flow with Conformal Penalty. ACM Trans. Graph. 39, 5, Article 161 (September 2020), 16 pages. DOI: https://doi.org/10.1145/3369387.

  5. Preprint Anthony Gruber, Magdalena Toda, Hung Tran. On the variation of curvature functionals in a space form with application to a generalized Willmore energy. Ann. Glob. Anal. Geom. (2019) 56: 147.
    DOI: https://doi.org/10.1007/s10455-019-09661-0.

Articles in Refereed Conference Proceedings

  1. Preprint Anthony Gruber, Eugenio Aulisa. Quaternionic Remeshing During Surface Evolution (to appear), Proceedings of the 18th International Conference of Numerical Analysis and Applied Mathematics, Rhodes, Greece 2020.

  2. Preprint Anthony Gruber, Magdalena Toda, Hung Tran. Willmore-Stable Minimal Surfaces (to appear), Proceedings of the 18th International Conference of Numerical Analysis and Applied Mathematics, Rhodes, Greece 2020.

  3. Preprint Eugenio Aulisa, Anthony Gruber, Magdalena Toda, Hung Tran. New Developments on the p-Willmore Energy of Surfaces, Proceedings of the XXIst Conference on Geometry, Integrability and Quantization, BAS - Varna 2019. DOI: https://doi.org/10.7546/giq-21-2020-57-65.

  4. Preprint Robert A. Bridges, Anthony D. Gruber, Christopher Felder, Miki Verma, Chelsey Hoff. Active Manifolds: A non-linear analogue to Active Subspaces. Volume 97: International Conference on Machine Learning (2019).

Others

  1. Here Anthony Gruber. Curvature functionals and p-Willmore energy. PhD Thesis (2019). TTU Electronic Thesis and Dissertation Repository.

Submitted Articles

  1. Preprint Yuankai Teng, Zhu Wang, Lili Ju, Anthony Gruber, Guannan Zhang. Learning Level Sets with Pseudo-Reversible Neural Networks for Nonlinear Dimension Reduction in Function Approximation, (under review).

  2. Preprint Anthony Gruber, Max Gunzburger, Lili Ju, Zhu Wang. A Comparison of Neural Network Architectures for Data-Driven Reduced-Order Modeling, (under review).

  3. Preprint Anthony Gruber, Eugenio Aulisa. Quasiconformal Mappings for Surface Mesh Optimization, (under revision).

  4. Preprint Anthony Gruber, Álvaro Pámpano, Magdalena Toda. On p-Willmore Disks with Boundary Energies, (under review).

  5. Preprint Anthony Gruber. Parallel Codazzi tensors with submanifold applications, (under review).

  6. Preprint Anthony Gruber, Magdalena Toda, Hung Tran. Stationary surfaces with boundaries, (under review).

 

Corrigenda to Published Works


All Arxiv preprints are kept up-to-date with this list. If you notice any typos/errors (or suspected errors) in the above publications, e-mail notifications are appreciated.

In Planar Immersions with Prescribed Curl and Jacobian Determinant are Unique.

  • Section 2, Paragraph 1:

                    \(\mathbf{v} \otimes \mathbf{v} - 2|\mathbf{v}|^2\,1\) \(\,\,\longrightarrow\,\,\) \(\mathbf{v} \otimes \mathbf{v} - |\mathbf{v}|^2\,1\) .

In On the variation of curvature functionals in a space form with application to a generalized Willmore energy.

  • Equation (22), line 2:

                    \(\frac{1}{2}\langle \nabla |h|^2, \nabla f\rangle\) \(\,\,\longrightarrow\,\,\) \(\frac{1}{2}u \langle \nabla |h|^2, \nabla f\rangle\) .

  • Equation (35), line 3:

                    \(- h^{ij}(\delta\Gamma^k_{ij})f_k + h^{ij}g^{kl}(u_ih_{jl}+u_jh_{il}-u_lh_{ij})f_k\) \(\,\,\longrightarrow\,\,\) \(-h^{ij}(\delta\Gamma^k_{ij})f_k\) .