In this work, we investigate the existence of compact free boundary minimal hypersurfaces immersed in several domains. Using an original integral identity for that are a domain whose is regular level set, study case where quadric or, more generally, rotational domain. This done without topological restrictions. We also obtain new gap theorem Euclidean ball and ellipsoid.

Abstract We give a combinatorial characterization of amenability monomial algebras and prove the existence Følner sequences, answering question due to Ceccherini–Silberstein Samet–Vaillant. then use our that over projectively simple algebras, every module is exhaustively amenable; we conclude convolution minimal subshifts admit same property. deduce any subshift positive entropy gives rise grad...

In this paper, we study the Gauss map of a free boundary minimal surface. The main theorem asserts that if components are eigenfunctions Jacobi-Steklov operator, then surface must be rotationally symmetric.

We extend the “linearly exponential” bound for the Castelnuovo-Mumford regularity of a graded ideal in a polynomial ring K[x1, . . . , xr] over a field (established by Galligo and Giusti in characteristic 0 and recently, by Caviglia-Sbarra for abitrary K) to graded submodules of a graded module over a homogeneous Cohen-Macaulay ring R = ⊕n≥0Rn with artinian local base ring R0. As an application...