A two-piece property for free boundary minimal surfaces in the ball
Vanderson Lima, Ana Menezes
We prove that every plane passing through the origin divides an embedded compact free boundary minimal surface of the euclidean 3-ball in exactly two connected surfaces. We also show that if a region in the ball has mean convex boundary and contains a nullhomologous diameter, then this region is a closed halfball. Moreover, we prove the regularity at the corners of currents minimizing a partially free boundary problem by following ideas by Grüter and Simon. Our first result gives evidence to a conjecture by Fraser and Li.
Transactions of the American Mathematical Society
https://doi.org/10.1090/tran/8223
10.1090/tran/8223
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Minimal surface Mathematics 100%
Free Boundary Mathematics 93%
Ball Mathematics 75%
Free Boundary Problem Mathematics 49%
Divides Mathematics 45%
Evidence Mathematics 39%
Euclidean Mathematics 38%
Closed Mathematics 27%
Lima, V., & Menezes, A. (2021). A two-piece property for free boundary minimal surfaces in the ball. Transactions of the American Mathematical Society, 374(3), 1661-1686. https://doi.org/10.1090/tran/8223
Lima, Vanderson ; Menezes, Ana. / A two-piece property for free boundary minimal surfaces in the ball. In: Transactions of the American Mathematical Society. 2021 ; Vol. 374, No. 3. pp. 1661-1686.
@article{3a3a56387a7443c48ef773dc423e727a,
title = "A two-piece property for free boundary minimal surfaces in the ball",
abstract = "We prove that every plane passing through the origin divides an embedded compact free boundary minimal surface of the euclidean 3-ball in exactly two connected surfaces. We also show that if a region in the ball has mean convex boundary and contains a nullhomologous diameter, then this region is a closed halfball. Moreover, we prove the regularity at the corners of currents minimizing a partially free boundary problem by following ideas by Gr{\"u}ter and Simon. Our first result gives evidence to a conjecture by Fraser and Li.",
author = "Vanderson Lima and Ana Menezes",
note = "Publisher Copyright: {\textcopyright} 2021 American Mathematical Society. All rights reserved.",
doi = "10.1090/tran/8223",
journal = "Transactions of the American Mathematical Society",
publisher = "American Mathematical Society",
Lima, V & Menezes, A 2021, 'A two-piece property for free boundary minimal surfaces in the ball', Transactions of the American Mathematical Society, vol. 374, no. 3, pp. 1661-1686. https://doi.org/10.1090/tran/8223
A two-piece property for free boundary minimal surfaces in the ball. / Lima, Vanderson; Menezes, Ana.
In: Transactions of the American Mathematical Society, Vol. 374, No. 3, 03.2021, p. 1661-1686.
T1 - A two-piece property for free boundary minimal surfaces in the ball
AU - Lima, Vanderson
AU - Menezes, Ana
N1 - Publisher Copyright: © 2021 American Mathematical Society. All rights reserved.
N2 - We prove that every plane passing through the origin divides an embedded compact free boundary minimal surface of the euclidean 3-ball in exactly two connected surfaces. We also show that if a region in the ball has mean convex boundary and contains a nullhomologous diameter, then this region is a closed halfball. Moreover, we prove the regularity at the corners of currents minimizing a partially free boundary problem by following ideas by Grüter and Simon. Our first result gives evidence to a conjecture by Fraser and Li.
AB - We prove that every plane passing through the origin divides an embedded compact free boundary minimal surface of the euclidean 3-ball in exactly two connected surfaces. We also show that if a region in the ball has mean convex boundary and contains a nullhomologous diameter, then this region is a closed halfball. Moreover, we prove the regularity at the corners of currents minimizing a partially free boundary problem by following ideas by Grüter and Simon. Our first result gives evidence to a conjecture by Fraser and Li.
U2 - 10.1090/tran/8223
DO - 10.1090/tran/8223
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
Lima V, Menezes A. A two-piece property for free boundary minimal surfaces in the ball. Transactions of the American Mathematical Society. 2021 Mar;374(3):1661-1686. https://doi.org/10.1090/tran/8223