1. Schwarz-Pick lemma for harmonic maps which are conformal at a pointFranc Forstnerič, David Kalaj, 2024, izvirni znanstveni članek Povzetek: We obtain a sharp estimate on the norm of the differential of a harmonic map from the unit disc ${\mathbb D}$ in ${\mathbb C}$ into the unit ball ${\mathbb B}^n$ in ${\mathbb R}^n$, $n\ge 2$, at any point where the map is conformal. In dimension $n=2$, this generalizes the classical Schwarz-Pick lemma, and for $n\ge 3$ it gives the optimal Schwarz-Pick lemma for conformal minimal discs ${\mathbb D}\to {\mathbb B}^n$. This implies that conformal harmonic immersions $M \to {\mathbb B}^n$ from any hyperbolic conformal surface are distance-decreasing in the Poincaré metric on $M$ and the Cayley-Klein metric on the ball ${\mathbb B}^n$, and the extremal maps are precisely the conformal embeddings of the disc ${\mathbb D}$ onto affine discs in ${\mathbb B}^n$. Motivated by these results, we introduce an intrinsic pseudometric on any Riemannian manifold of dimension at least three by using conformal minimal discs, and we lay foundations of the corresponding hyperbolicity theory.
Ključne besede: harmonic maps, minimal surfaces, Schwarz–Pick lemma, Cayley–Klein metric
Objavljeno v DiRROS: 25.04.2024; Ogledov: 59; Prenosov: 19
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2. Domains without parabolic minimal submanifolds and weakly hyperbolic domainsFranc Forstnerič, 2023, izvirni znanstveni članek Povzetek: We show that if $\Omega$ is an $m$-convex domain in $\mathbb{R}^n$ for some $2 \le m < n$ whose boundary $b\Omega$ has a tubular neighbourhood of positive radius and is not $m$-flat near infinity, then $\Omega$ does not contain any immersed parabolic minimal submanifolds of dimension $\ge m$. In particular, if $M$ is a properly embedded non-flat minimal hypersurface in $\mathbb{R}^n$ with a tubular neighbourhood of positive radius, then every immersed parabolic hypersurface in $\mathbb{R}^n$ intersects $M$. In dimension $n=3$, this holds if $M$ has bounded Gaussian curvature function. We also introduce the class of weakly hyperbolic domains $\Omega$ in $\mathbb{R}^n$, characterised by the property that every conformal harmonic map $\mathbb{C} \to \Omega$ is constant, and we elucidate their relationship with hyperbolic domains, and domains without parabolic minimal surfaces.
Ključne besede: minimal surfaces, m-plurisubharmonic functions, hyperbolic domain
Objavljeno v DiRROS: 10.04.2024; Ogledov: 74; Prenosov: 36
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3. The Calabi-Yau problem for minimal surfaces with Cantor endsFranc Forstnerič, 2023, izvirni znanstveni članek Povzetek: We show that every connected compact or bordered Riemann surface contains a Cantor set whose complement admits a complete conformal minimal immersion in ${\mathbb R}^3$ with bounded image. The analogous result holds for holomorphic immersions into any complex manifold of dimension at least $2$, for holomorphic null immersions into ${\mathbb C}^n$ with $n \ge 3$, for holomorphic Legendrian immersions into an arbitrary complex contact manifold, and for superminimal immersions into any selfdual or anti-self-dual Einstein four-manifold.
Ključne besede: minimal surfaces, Calabi–Yau problem, null curve, Legendrian curve
Objavljeno v DiRROS: 08.04.2024; Ogledov: 73; Prenosov: 35
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4. Proper holomorphic maps in Euclidean spaces avoiding unbounded convex setsBarbara Drinovec-Drnovšek, Franc Forstnerič, 2023, izvirni znanstveni članek Povzetek: We show that if $E$ is a closed convex set in $\mathbb C^n$, $n>1$ contained in a closed halfspace $H$ such that ▫$E\cap bH$▫ is nonempty and bounded, then the concave domain $\Omega=\mathbb C^n\setminus E$ contains images of proper holomorphicmaps $f : X \to \mathbb C^n$ from any Stein manifold $X$ of dimension $< n$, with approximation of a givenmap on closed compact subsets of $X$. If in addition $2 {\rm dim} X+1 \le n$ then $f$ can be chosen an embedding, and if $2 {\rm dim} X = n$, then it can be chosen an immersion. Under a stronger condition on $E$, we also obtain the interpolation property for such maps on closed complex subvarieties.
Ključne besede: Stein manifolds, holomorphic embeddings, Oka manifold, minimal surfaces, convexity
Objavljeno v DiRROS: 15.03.2024; Ogledov: 95; Prenosov: 48
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5. Minimal surfaces with symmetriesFranc Forstnerič, 2024, izvirni znanstveni članek Povzetek: Let $G$ be a finite group acting on a connected open Riemann surface $X$ by holomorphic automorphisms and acting on a Euclidean space ${\mathbb R}^n$ $(n\ge 3)$ by orthogonal transformations. We identify a necessary and sufficient condition for the existence of a $G$-equivariant conformal minimal immersion $F:X\to{\mathbb R}^n$. We show in particular that such a map $F$ always exists if $G$ acts without fixed points on $X$. Furthermore, every finite group $G$ arises in this way for some open Riemann surface $X$ and $n=2|G|$. We obtain an analogous result for minimal surfaces having complete ends with finite total Gaussian curvature, and for discrete infinite groups acting on $X$ properly discontinuously and acting on ${\mathbb R}^n$ by rigid transformations.
Ključne besede: Riemann surfaces, minimal surfaces, G-equivariant conformal minimal immersion
Objavljeno v DiRROS: 13.03.2024; Ogledov: 114; Prenosov: 42
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6. Effect of sucrose concentration on streptococcus mutans adhesion to dental material surfacesAnamarija Zore, Franc Rojko, Nives Matijaković Mlinarić, Jona Veber, Aleksander Učakar, Roman Štukelj, Andreja Pondelak, Andrijana Sever Škapin, Klemen Bohinc, 2024, izvirni znanstveni članek Povzetek: Enamel demineralization, known as dental caries, is instigated by the bacterium Streptococcus mutans, which generates acid during carbohydrate metabolism. Among carbohydrates, sucrose is the most cariogenic and capable of biofilm formation. This study aimed to explore and comprehend Streptococcus mutans’ adherence to two prevalent dental material surfaces, i.e., a cobalt–chromium(Co-Cr) alloy and a resin-based composite, under the influence of various sucrose concentrations. To understand bacterial adhesion, the surfaces were characterized using profilometry, tensiometry, and surface charge measurements. Bacterial adhesion was evaluated using scanning electron microscopy and crystal violet dye methods. Results revealed that the composite surface exhibited greater rough-ness compared with the Co-Cr alloy surface. Both surfaces displayed hydrophilic properties and a negative surface charge. Bacterial adhesion experiments indicated lower bacterial adherence to the Co-Cr alloy than to the composite surface before the addition of sucrose. However, the introduction of sucrose resulted in biofilm development on both surfaces, showcasing a similar increase in bacterial adhesion, with the highest levels being observed at a 5% sucrose concentration in the bacterial suspension. In conclusion, the findings suggest sucrose-rich foods could facilitate bacterial adaptation despite less favorable surface characteristics, thereby promoting biofilm formation.
Ključne besede: bacterial adhesion, streptococcus mutans, dental material surfaces, sucrose concentration
Objavljeno v DiRROS: 31.01.2024; Ogledov: 182; Prenosov: 67
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7. Biophysical properties of foamed and solid polymers used in orthotics and prostheticsKlemen Bohinc, Anže Abram, Anamarija Zore, Roman Štukelj, Ana Lenarčič, Rajko Vidrih, Andrijana Sever Škapin, 2021, izvirni znanstveni članek Povzetek: Orthotic and prosthetic materials should have good mechanical and antibacterial properties. Therefore, in our study, we consider four common foamed closed-cells and two solid polymeric materials regarding their mechanical behaviour and tendency for bacterial adhesion. For all materials, the surface roughness, hydrophobicity, zeta potential, tensile properties, hardness and CIE color parameters were measured. We found that foamed polymeric materials have higher roughness, higher hydrophobicity, lower Young's modulus, lower maximum tensile strength and lower hardness than solid materials. Bacterial adhesion test measurements based on observation by scanning electron microscopy show much a lower adhesion extent of S. aureus on solid materials than on foamed materials. The measured biophysical properties could be the key data for users to select the optimal materials.
Ključne besede: surface characterization, bacterial adhesion, foamed materials, prosthetic and orthotic material, surfaces
Objavljeno v DiRROS: 22.05.2023; Ogledov: 259; Prenosov: 169
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8. Deposition of chitosan on plasma-treated polymers : a reviewAlenka Vesel, 2023, pregledni znanstveni članek Povzetek: Materials for biomedical applications often need to be coated to enhance their performance, such as their biocompatibility, antibacterial, antioxidant, and anti-inflammatory properties, or to assist the regeneration process and influence cell adhesion. Among naturally available substances, chitosan meets the above criteria. Most synthetic polymer materials do not enable the immobilization of the chitosan film. Therefore, their surface should be altered to ensure the interaction between the surface functional groups and the amino or hydroxyl groups in the chitosan chain. Plasma treatment can provide an effective solution to this problem. This work aims to review plasma methods for surface modification of polymers for improved chitosan immobilization. The obtained surface finish is explained in view of the different mechanisms involved in treating polymers with reactive plasma species. The reviewed literature showed that researchers usually use two different approaches: direct immobilization of chitosan on the plasma-treated surface or indirect immobilization by additional chemistry and coupling agents, which are also reviewed. Although plasma treatment leads to remarkably improved surface wettability, this was not the case for chitosan-coated samples, where a wide range of wettability was reported ranging from almost superhydrophilic to hydrophobic, which may have a negative effect on the formation of chitosan-based hydrogels.
Ključne besede: polymer surfaces, chitosan, coatings, plasma-surface modification, adhesion
Objavljeno v DiRROS: 24.02.2023; Ogledov: 400; Prenosov: 218
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