Using the US as an example, most violent crime is concentrated in cities. If you look at this map (https://lawstreetmedia.com/news/crime-america-2016-interactive-crime-map-metro-areas-united-states/) you can get an idea of where violent crime is most concentrated.
Generally, the concentration of violence doesn't affect entire cities, but can impact development/growth in city segments/neighborhoods. But, that also depends on the characteristics of neighborhoods and factors affecting neighborhood resilience (as an example see, Sampson, Robert J. Great American city: Chicago and the enduring neighborhood effect. University of Chicago Press, 2012.) Certainly, there may be exceptions where economic growth declines and high levels of violence co-exist in cities, such as, perhaps, in Gary, Indiana or Detroit, Michigan. Typically, in criminology, declining growth but especially economic inequality would be linked to changes in crime. Your question raises the interesting possibility that crime has a feedback mechanism that limits economic growth. That question has not been widely studied.
This study uses data from Italy, and finds that " On average, a rise in crime rates by 1% reduces the real economic growth by 0.00040% in a month" and that "During a recession (expansion), a rise in crime by 1% causes, on average, a change by - 0.00022% in annual GDP growth, which corresponds to a reduction of 2.6 million euros (2.4 million euros) in a year. In practice, the long run crime costs are 5% higher during recession than expansion."
Thank you very much, your contribution was perfect. I am building the theoretical framework on the subject. If you have other literatures you can indicate it will be welcome. Regards,
Since Raid answered, this reminded me that he has done a study on rape clusters in the United States. One of the things you would note in looking at that study is how large some of the rape clusters are -- expanding well beyond city boundaries.
Article Geographical Clusters of Rape in the United States: 2000-201...
The scary part of it is that after creating cluster maps you can easily verify each cluster by using Google. It shows up as clear as the sun. I then tell myself "statistics really works".