APPEARING on “So You Think You Can Dance”, an American TV show, Jennifer Lopez starts her song “Louboutins” by lying sulkily in sheets of red silk on a bed in a giant sparkly shoe and making a phone call. “Hello, Santa,” she says, batting her eyelashes, “I would like a shiny new pair of Louboutin shoes. You know, the ones with the high heels and red bottoms.”

In the 20 years since Christian Louboutin made his first pair of ladies' shoes with shiny red-lacquered soles, his vertiginously heeled, sexy, colourful and nearly unwearable creations have become an object of desire for celebrities like Ms Lopez, Angelina Jolie and Madonna, who even lets her daughter Lourdes wear a metal-studded number. Today the puckish Frenchman is the biggest star in high-fashion shoe design, selling about 240,000 pairs a year in America at prices ranging from $395 for espadrilles to as much as $6,000 for a “super-platform” pump covered in crystals. The revenue of his company, Louboutin, is forecast at $135m this year.

Yet all this could be at risk, says Louboutin's lawyer, if Yves Saint Laurent (YSL), another fashion firm, continues to gain the upper hand in a legal dispute between the two companies. On August 10th a district court in New York refused to grant a preliminary injunction stopping YSL from selling shoes with a red sole that Louboutin says infringe its trademark. The judge did not believe that a designer could trademark a colour. He asked both parties to appear again in court on August 19th to decide how to proceed with the case.

“We don't like it,” says Harley Lewin of McCarter & English, an American law firm which is representing Louboutin. The judge has overreached, according to Mr Lewin, by making this a case about the justification of Louboutin's trademark rather than a ruling on a request for a temporary injunction prohibiting the sale of red-soled YSL shoes. He intends to appeal against the decision.

Louboutin sued YSL alleging that several of its rival's shoes infringed Louboutin's trademark on women's shoes with a red outsole, which was granted to the company in 2008 by America's Patent and Trademark Office. Louboutin identifies the shade it uses as “Chinese red”, but argues that any confusingly similar shade would infringe the trademark. YSL's offending shoes are red all over.

In denying the request for an injunction the judge said that in the fashion industry colour serves ornamental and aesthetic functions vital to robust competition, so Louboutin was unlikely to be able to prove that its brand was entitled to trademark protection. He acknowledged that courts had recognised the use of colour in trademarks in the fashion industry before, but only in patterns with multiple designs such as the Louis Vuitton logo or Burberry check. Trademarks have been given to single colours for industrial products, such as yellow for Post-it notes.

Louboutin retorts that granting a trademark to one or several colours, such as Gucci's stripes, is the same. Moreover, it maintains that Christian Louboutin was the first to use red outsoles. Not true, says its opponent, who claims that King Louis XIV had red-heeled dancing shoes in the 18th century and Dorothy danced in ruby slippers in “The Wizard of the Oz”.

The judge has made up his mind that no fashion designer should be allowed a monopoly on colour because as artists they all need to be able to use the full palette. To make this point, he imagined Picasso taking Monet to court over the use of blue in his painting of water lilies, because it was the same or close to the distinctive shade of indigo, the “colour of melancholy” he used in his Blue Period. Moreover, unlike patent law, trademarks are never about granting monopolies, argues David Bernstein, a lawyer for YSL at Debevoise and Plimpton. Trademarks are merely the right to indicate the origin of a product or service.

Susan Scafidi of Fordham University School of Law in New York says that the judge sidestepped the important question by boiling the argument down to aesthetic functionality. The true challenge of the case, says Ms Scafidi, is to determine when the use of colour on a portion of apparel is a design element and when it is a trademark. It will now be the job of an appeal court to rule on the matter. And if Louboutin loses again, the company says it will take its case all the way to the Supreme Court.