Min-max theory for GG-invariant minimal hypersurfaces

In this paper, we consider a closed Riemannian manifold $M^{n+1}$ with dimension $3\leq n+1\leq 7$, and a compact Lie group $G$ acting as isometries on $M$ with cohomogeneity at least $3$. After adapting the Almgren-Pitts min-max theory to a $G$-equivariant version, we show the existence of a nontrivial closed smooth embedded $G$-invariant minimal hypersurface $\Sigma\subset M$ provided that the union of non-principal orbits forms a smooth embedded submanifold of $M$ with dimension at most $n-2$. Moreover, we also build upper bounds as well as lower bounds of $(G,p)$-width which are analogs of the classical conclusions derived by Gromov and Guth. An application of our results combined with the work of Marques-Neves shows the existence of infinitely many $G$-invariant minimal hypersurfaces when ${\rm Ric}_M>0$ and orbits satisfy the same assumption above

Min-max theory for free boundary G-invariant minimal hypersurfaces

Given a compact Riemannian manifold $M^{n+1}$ with dimension $3\leq n+1\leq 7$ and $\partial M\neq\emptyset$, the free boundary min-max theory built by Martin Man-Chun Li and Xin Zhou shows the existence of a smooth almost properly embedded minimal hypersurface with free boundary in $\partial M$. In this paper, we generalize their constructions into equivariant settings. Specifically, let $G$ be a compact Lie group acting as isometries on $M$ with cohomogeneity at least $3$. Then we show that there exists a nontrivial smooth almost properly embedded $G$-invariant minimal hypersurface with free boundary. Moreover, if the Ricci curvature of $M$ is non-negative and $\partial M$ is strictly convex, then there exist infinitely many properly embedded $G$-invariant minimal hypersurfaces with free boundary.Comment: Accepted by Advances in Mathematic

Min-max theory for free boundary minimal hypersurfaces in locally wedge-shaped manifolds

We develop a min-max theory for the area functional in the class of locally wedge-shaped manifolds. Roughly speaking, a locally wedge-shaped manifold is a Riemannian manifold that is allowed to have both boundary and certain types of edges. Fix a dimension $3 \le n+1 \le 6$. As our main theorem, we prove that every compact locally wedge-shaped manifold $M^{n+1}$ with acute wedge angles contains a locally wedge-shaped free boundary minimal hypersurface $\Sigma^n$ which is smooth in its interior and on its faces and is $C^{2,\alpha}$ up to and including its edge. We can also handle the case of 90 degree wedge angles under an additional assumption.Comment: 47 pages, 6 figures, comments are welcome

Generalized S1S^1-stability theorem

We use the equivariant $\mu$-bubbles technique to prove that for any compact manifold $M^n$ with non-empty boundary, $n\in\{3,5,6\}$, the Yamabe invariant of $M^n$ is positive if and only if the Yamabe invariant of $M^n\times S^1$ is positive. This generalized the $S^1$-stability conjecture of Rosenberg to compact manifolds with boundary.Comment: 14 pages, comments are welcome

Curvature estimates for stable free boundary minimal hypersurfaces in locally wedge-shaped manifolds

In this paper, we consider locally wedge-shaped manifolds, which are Riemannian manifolds that are allowed to have both boundary and certain types of edges. We define and study the properties of free boundary minimal hypersurfaces inside locally wedge-shaped manifolds. In particular, we show a compactness theorem for free boundary minimal hypersurfaces with curvature and area bounds in a locally wedge-shaped manifold. Additionally, using Schoen-Simon-Yau's estimates, we also prove a Bernstein-type theorem indicating that, under certain conditions, a stable free boundary minimal hypersurface inside a Euclidean wedge must be a portion of a hyperplane. As our main application, we establish a curvature estimate for sufficiently regular free boundary minimal hypersurfaces in a locally wedge-shaped manifold. We expect this curvature estimate will be useful for establishing a min-max theory for the area functional in wedge-shaped spaces.Comment: 28 pages, 6 figures, comments are welcome

Stabilization of Fast Pyrolysis Liquids from Biomass by Mild Catalytic Hydrotreatment:Model Compound Study

Repolymerization is a huge problem in the storage and processing of biomass pyrolysis liquid (PL). Herein, to solve the problem of repolymerization, mild catalytic hydrotreatment of PL was conducted to convert unstable PL model compounds (hydroxyacetone, furfural, and phenol) into stable alcohols. An Ni/SiO2 catalyst was synthesized by the deposition-precipitation method and used in a mild hydrotreatment process. The mild hydrotreatment of the single model compound was studied to determine the reaction pathways, which provided guidance for improving the selectivity of stable intermediate alcohols through the control of reaction conditions. More importantly, the mild hydrotreatment of mixed model compounds was evaluated to simulate the PL more factually. In addition, the effect of the interaction between hydroxyacetone, furfural, and phenol during the catalytic hydrotreatment was also explored. There was a strange phenomenon observed in that phenol was not converted in the initial stage of the hydrotreatment of mixed model compounds. Thermogravimetric analysis (TGA), Ultraviolet-Raman (UV-Raman), and Brunauer−Emmett−Teller (BET) characterization of catalysts used in the hydrotreatment of single and mixed model compounds demonstrated that this phenomenon did not mainly arise from the irreversible deactivation of catalysts caused by carbon deposition, but the competitive adsorption among hydroxyacetone, furfural, and phenol during the mild hydrotreatment of mixed model compounds

Rapid screening of Salmonella enterica serovars Enteritidis, Hadar, Heidelberg and Typhimurium using a serologically-correlative allelotyping PCR targeting the O and H antigen alleles

<p>Abstract</p> <p>Background</p> <p>Classical <it>Salmonella </it>serotyping is an expensive and time consuming process that requires implementing a battery of O and H antisera to detect 2,541 different <it>Salmonella enterica </it>serovars. For these reasons, we developed a rapid multiplex polymerase chain reaction (PCR)-based typing scheme to screen for the prevalent <it>S. enterica </it>serovars Enteritidis, Hadar, Heidelberg, and Typhimurium.</p> <p>Results</p> <p>By analyzing the nucleotide sequences of the genes for O-antigen biosynthesis including <it>wb</it>a operon and the central variable regions of the H1 and H2 flagellin genes in <it>Salmonella</it>, designated PCR primers for four multiplex PCR reactions were used to detect and differentiate <it>Salmonella </it>serogroups A/D1, B, C1, C2, or E1; H1 antigen types i, g, m, r or z₁₀; and H2 antigen complexes, I: 1,2; 1,5; 1,6; 1,7 or II: e,n,x; e,n,z₁₅. Through the detection of these antigen gene allele combinations, we were able to distinguish among <it>S. enterica </it>serovars Enteritidis, Hadar, Heidelberg, and Typhimurium. The assays were useful in identifying <it>Salmonella </it>with O and H antigen gene alleles representing 43 distinct serovars. While the H2 multiplex could discriminate between unrelated H2 antigens, the PCR could not discern differences within the antigen complexes, 1,2; 1,5; 1,6; 1,7 or e,n,x; e,n,z₁₅, requiring a final confirmatory PCR test in the final serovar reporting of <it>S. enterica</it>.</p> <p>Conclusion</p> <p>Multiplex PCR assays for detecting specific O and H antigen gene alleles can be a rapid and cost-effective alternative approach to classical serotyping for presumptive identification of <it>S. enterica </it>serovars Enteritidis, Hadar, Heidelberg, and Typhimurium.</p

Photoemission Evidence of a Novel Charge Order in Kagome Metal FeGe

A charge order has been discovered to emerge deep into the antiferromagnetic phase of the kagome metal FeGe. To study its origin, the evolution of the low-lying electronic structure across the charge order phase transition is investigated with angle-resolved photoemission spectroscopy. We do not find signatures of nesting between Fermi surface sections or van-Hove singularities in zero-frequency joint density of states, and there are no obvious energy gaps at the Fermi level, which exclude the nesting mechanism for the charge order formation in FeGe. However, two obvious changes in the band structure have been detected, i.e., one electron-like band around the K point and another one around the A point move upward in energy position when the charge order forms. These features can be well reproduced by our density-functional theory calculations, where the charge order is primarily driven by magnetic energy saving via large dimerizations of a quarter of Ge1-sites (in the kagome plane) along the c-axis. Our results provide strong support for this novel charge order formation mechanism in FeGe, in contrast to the conventional nesting mechanism.Comment: 6 pages, 4 figure