Embedded minimal tori in S3 and the Lawson conjecture

By S. Brendle. 2012

186 citations recorded by the source corpus.

We show that any embedded minimal torus in S3 is congruent to the Clifford torus. This answers a question posed by H. B. Lawson, Jr., in 1970.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/5a2f914a73ec1e613071abcf4acc48fe0e6fa47a

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Compactness of the space of embedded minimal surfaces with free boundary in three-manifolds with nonnegative Ricci curvature and convex boundary (2012, result): “S3 up to congruences. Various partial results were obtained in this direction with additional assumptions ([31] [28] [23]). Very recently, Lawson’s conjecture was proved in full generality by Brendle [4]. In this paper, we prove that the space of properly embedded minimal surfaces in B3 with free bo”
Embedded self-similar shrinkers of genus 0 (2014, background): “This conjecture was recently conﬁrmed in [3]; see [6] for a survey.”
Minimal surfaces in $$S^3$$: a survey of recent results (2013, background): “tated in a paper by Sheng and Wang in [48]; the result is a direct consequence of the work of White on the structure of singularities in the mean curvature ﬂow (cf. [54], [55], [56]). The argument in [9] uses a diﬀerent quantity, which involves the norm of the second fundamental form. A major diﬃcul”
Moduli of continuity, isoperimetric profiles, and multi-point estimates in geometric heat equations (2014, methodology): “THE LAWSON AND PINKALL-STERLING CONJECTURES AND RELATED RESULTS Finally, I will explain how the non-collapsing argument can be applied to minimal tori in the three-sphere, a beautiful insight of Simon Brendle [29]: Lawson conjectured in 1970 that an embedded minimal torus in the three-dimensional sp”
A sharp bound for the inscribed radius under mean curvature flow (2013, background): “me common features with [1]. However, we are able to gain an extra gradient term in the evolution equation. A similar gradient term played a crucial role in our solution of the Lawson Conjecture (cf. [3], [4], [5], [6]). In Section 3, we estimate the Laplacian ∆µ from below. In Section 4, we prove L”
A Characterization of the Critical Catenoid (2016, background): “Before Brendle’s proof, earlier work of Ros had established that the conclusion of the Lawson conjecture held with an additional strong assumption of symmetry with respect to the coordinate planes.”
Minimal Surfaces in the Round Three‐Sphere by Doubling the Equatorial Two‐Sphere, II (2014, result): “es in the round three-sphere S3(1), especially of those of area close to 8πor less, is a natural open question. This is further motivated by the recent resolutions of the Lawson conjecture by Brendle [2] and the Willmore conjecture by Marques and Neves [18] where they also characterize the Cliﬀord t”