Spectators walk through the shadows of the Olympic rings at Olympic Park. (Mark Baker/AP)

The glistening new Gorky Gorod Mall here features both a Cinnabon and a Subway, just down the escalator from the Lucky Strike bowling alley and across from a luxury furrier adjacent to a jewelry store, “Diamond Paradise.” Among them all are storefronts bearing signs saying, in both Russian and English, “Opening Soon.”

In the spaces that are supposed to be new stores lie piles of empty cardboard boxes, broken drywall, twisted wire and dust.

If the opening of the Winter Games here at the mountain venues and 40 miles to the south in Sochi was about organizers’ preparedness — or lack thereof — then the final weekend could easily leave athletes and tourists alike wondering what will become of this $50 billion investment once the circus leaves town.

Next week, the Rosa Khutor ski resort — which has hosted Alpine racing and all manner of sliding events and extreme snow sports — will sit closed to the public. The six massive arenas that make up the Olympic Park in the Adler district of Sochi will be empty. And though organizers maintain that there is a post-Games plan for everything, there is skepticism because unlike Vancouver or Salt Lake City — past hosts of Winter Olympics — there was essentially nothing like this here even a year ago.

“When we went to Krasnaya Polyana to watch biathlon, we were wondering what would happen to all these hotels,” said Inga Polyachek, an entrepreneur from Sochi. “There are so many of them, and I have to say this issue is a concern.”

Though the Black Sea resort of Sochi has long been a destination for summer holidays, there is no significant history of Russian tourism in the Caucasus Mountains for winter sports — other than President Vladimir Putin, who convinced the International Olympic Committee to grant the Games to Sochi and famously skis here. The highway from Sochi to the mountains is new. The railroad from Sochi to the mountains is new. Add all that to the Olympic Park, which sits roughly 15 miles from central Sochi, and there is some question about what use it will all be going forward.

“They bit off a lot,” said Lisa Delpy Neirotti, a sports management professor at George Washington University who studies how cities can leverage hosting the Olympics. “They developed a whole city, basically, and that was far more than they needed for the Olympic Games.”

Sochi officials insist there is a plan in place both for the venues built specifically for the Games and the mountain resort that sprung up, almost from thin air, over the past year. The main media center, they say, will be turned into a mall. The Fisht Olympic Stadium, which hosts only the Opening and Closing Ceremonies, will be the site of soccer games during the 2018 World Cup, which will be staged across Russia. The speedskating venue is slated to become an exhibition hall. In October, the entire Olympic Park will hold a Formula 1 auto race, the first of seven annual races to be held there.

“There will be no white elephants,” said Dmitry Chernyshenko, the president of the Sochi 2014 Olympic Organizing Committee.

Still, just a week prior to the Opening Ceremonies, Prime Minister Dmitry Medvedev issued an order on the government’s Web site urging that officials come up with a viable plan for all of the Olympic venues. And it’s not just the sports arenas that could seem superfluous; some 40,000 hotel rooms were dedicated to the Olympics, more than 20,000 of which were new, according to Sochi 2014 officials. This is in a Russian economy that Mark Kramer of Harvard University’s Davis Center for Russian and Eurasian Studies said is likely to grow slowly over the next several years.

“I doubt Putin is going to want to channel large amounts of scarce funding to bolstering all these facilities once the Olympics are over and begin to fade from memory,” Kramer said in an e-mail. “Putin has channeled ample funds to his native city, St. Petersburg/Leningrad, and he is fond of Sochi, but in the list of priorities, it’s not going to rank high. Hence, I expect that Sochi will end up with a lot of facilities and hotels that are going to be pretty useless five years from now.”

Neirotti spent time at the Olympics with 26 of her students researching the Games, their facilities, the fans who came and what the future might hold. Though their survey results aren’t final, they found little evidence of marketing the resort as an international tourism destination. That includes the mountain cluster, where the hotels at the top of a gondola ride — billed as “Level +960” — have just-opened dining rooms that are far less than half full during peak dinner hours, even during the Olympics, when most of the rooms are occupied.

Attracting bodies when the ski resort opens to the public March 22 could be an issue, too. The sprawling, new Marriott hotel that sits a short walk from the base of the gondola has rooms available for 4,500 rubles a night — about $125 dollars — when the ski lifts open to the public.

“We have no doubt whatsoever that this resort will ultimately survive and will stay a ski resort,” said Sergey Belikov, a manager of the Rosa Khutor resort. “We have no doubt whatsoever that this will be commercially viable.”

Others are unsure.

“I doubt that ordinary Russians will have any idea on that or will be interested,” said Lilia Shevtsova, a senior associate at the Carnegie Moscow Center’s Russian Domestic Politics and Political Institutions Program. “This is the project for rich people. The latter hardly will be interested either because they will find it more safe to have vacation or engage in sport activity in the Alps but not in the vicinity of the Northern Caucasus. . . . The rest will be a new ghost city.”

More than a decade of political unrest in the region, originally stemming from conflicts between Russia and the breakaway state of Chechnya to the southeast of Sochi, also could make tourism in the Caucasus unpalatable. During the Olympics, armed soldiers have manned small lookout huts along the roads leading to the Alpine skiing venue.

There are examples of other cities that have failed to find uses for their Olympic facilities after hosting a Games; Athens stands out. Others have thrived; Salt Lake City is a success story. Sochi, though, is unique because of its expense and new infrastructure — both unprecedented.

“The Games are always just used as a catalyst,” Neirotti said. “It’s not really the end-all for most of these cities. It’s just the way to get something done. If Putin keeps working the plan to build the region down here, then it will be successful.

“But if after Putin leaves or if he changes his mind or priorities and they pull out money or pull out marketing strategy, then we’re going to come back and see it all as a wasteland.”

On Thursday afternoon, workers continued to scurry about this mountain community, which didn’t exist a year ago. One painted a railing in front of a hotel. Two more carried velvet ropes, wrapped in plastic, into the mall. Another walked with a bucket of mortar and a masonry trowel. With three days to go in the Olympics, there remained lots of work to be done. To what end, people here aren’t sure.

“I really don’t know how are they going to use it all,” said Polyachek, the Sochi resident. “When we have snow, Kransya Polyana exists and works. But when there is no snow, there is no Krasnaya Polyana.”

Natasha Abbakumova in Sochi contributed to this report.