$$O(n)\times O(m)$$-invariant hypersurfaces with constant mean curvature in Euclidean space
Abstract We prove some estimates for the infimum and supremum of the squared norm of the second fundamental form of $$O(n)\times O(m)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:mi>n</mml:mi> <mml:mo>)</mml:mo> <mml:mo>×</mml:mo> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:mi>m</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> -invariant hypersurfaces in $$\mathbb {R}^{n+m}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>+</mml:mo> <mml:mi>m</mml:mi> </mml:mrow> </mml:msup> </mml:math> with constant mean curvature $$H>0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>H</mml:mi> <mml:mo>></mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> .
Authors
- Josué Meléndez (ORCID: https://orcid.org/0000-0002-3257-985X)
- Eduardo Rodríguez-Romero (ORCID: https://orcid.org/0009-0007-1205-5657)
Institutions
- Universidad Autónoma Metropolitana (MX)
Publication Details
- Journal
- Rendiconti del Circolo Matematico di Palermo Series 2
- Published
- 2025-08-11
- DOI
- https://doi.org/10.1007/s12215-025-01302-9
- Primary Topic
- Geometric Analysis and Curvature Flows
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Consejo Nacional de Ciencia y Tecnología
- Universidad Autónoma Metropolitana unidad Iztapalapa